Edit Profile (opens in new tab) Ponce, Gustavo Compute Distance To: Compute Author ID: ponce.gustavo Published as: Ponce, Gustavo; Ponce, G. Homepage: http://www.math.ucsb.edu/~ponce/ External Links: MGP · Wikidata · ResearchGate · GND Documents Indexed: 121 Publications since 1983, including 2 Books 3 Contributions as Editor Biographic References: 1 Publication Co-Authors: 45 Co-Authors with 104 Joint Publications 1,258 Co-Co-Authors all top 5 Co-Authors 20 single-authored 50 Vega, Luis 48 Kenig, Carlos Eduardo 28 Linares, Felipe 11 Escauriaza Zubiria, Luis 6 Fonseca, Germán Eduardo 5 Isaza, Pedro 5 Kato, Tosio 5 Saut, Jean-Claude 3 Bekiranov, Daniella 3 Bona, Jerry Lloyd 3 Muñoz, Claudio 3 Ogawa, Takayoshi 3 Sideris, Thomas C. 2 Angulo Pava, Jaime 2 Birnir, Bjorn 2 Dafermos, Constantin 2 Frid, Hermano 2 Himonas, A. Alexandrou 2 Liu, Tai-Ping 2 Misiołek, Gerard 2 Nahas, Joules 2 Pilod, Didier 2 Racke, Reinhard 2 Rolvung, Christian 2 Santos, Gleison N. 2 Svanstedt, Nils E. M. 1 Cordes, Heinz Otto 1 Cowling, Michael G. 1 Dawson, Liana L. 1 Jensen, Arne 1 Klainerman, Sergiu 1 Kuroda, Shige Toshi 1 Lim, Wee Keong 1 McGahagan, Helena 1 Mendez, Argenis J. 1 Mitrea, Marius 1 Miyazaki, Hayato 1 Scialom, Marcia 1 Simon, Barry 1 Smith, Derek L. 1 Sparber, Christof 1 Taylor, Michael Eugene 1 Titi, Edriss Saleh 1 Tom, Michael Mudi 1 Zhou, Yong all top 5 Serials 9 Communications in Mathematical Physics 8 Journal of Functional Analysis 8 Proceedings of the American Mathematical Society 8 Communications in Partial Differential Equations 7 Journal of Differential Equations 5 Duke Mathematical Journal 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Communications on Pure and Applied Mathematics 4 Mathematical Research Letters 4 Bulletin of the Brazilian Mathematical Society. New Series 3 Transactions of the American Mathematical Society 3 SIAM Journal on Mathematical Analysis 2 Advances in Mathematics 2 Indiana University Mathematics Journal 2 Inventiones Mathematicae 2 Journal of the London Mathematical Society. Second Series 2 Journal of the American Mathematical Society 2 Journal of Dynamics and Differential Equations 2 Nonlinear Analysis. Theory, Methods & Applications 2 Universitext 1 Acta Cientifica Venezolana 1 Journal of Mathematical Analysis and Applications 1 Nonlinearity 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Mathematische Annalen 1 Revista Matemática Iberoamericana 1 Differential and Integral Equations 1 IMRN. International Mathematics Research Notices 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Bulletin of the American Mathematical Society. New Series 1 Notices of the American Mathematical Society 1 Advances in Differential Equations 1 Discrete and Continuous Dynamical Systems 1 Documenta Mathematica 1 Matemática Contemporânea 1 The Asian Journal of Mathematics 1 RIMS Kokyuroku 1 Journal of the European Mathematical Society (JEMS) 1 Acta Mathematica Sinica. English Series 1 Communications in Contemporary Mathematics 1 Annales Henri Poincaré 1 Communications on Pure and Applied Analysis 1 RIMS Kôkyûroku Bessatsu 1 São Paulo Journal of Mathematical Sciences all top 5 Fields 122 Partial differential equations (35-XX) 22 Fluid mechanics (76-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 Functional analysis (46-XX) 3 General and overarching topics; collections (00-XX) 2 Operator theory (47-XX) 2 Numerical analysis (65-XX) 2 Optics, electromagnetic theory (78-XX) 1 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 113 Publications have been cited 5,300 times in 3,063 Documents Cited by ▼ Year ▼ Commutator estimates and the Euler and Navier-Stokes equations. Zbl 0671.35066Kato, Tosio; Ponce, Gustavo 840 1988 Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Zbl 0808.35128Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 591 1993 A bilinear estimate with applications to the KdV equation. Zbl 0848.35114Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 343 1996 Oscillatory integrals and regularity of dispersive equations. Zbl 0738.35022Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 311 1991 Well-posedness of the initial value problem for the Korteweg-de Vries equation. Zbl 0737.35102Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 293 1991 The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices. Zbl 0787.35090Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 175 1993 On the ill-posedness of some canonical dispersive equations. Zbl 1034.35145Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 160 2001 Global existence of small solutions to a class of nonlinear evolution equations. Zbl 0576.35023Ponce, Gustavo 157 1985 Persistence properties and unique continuation of solutions of the Camassa-Holm equation. Zbl 1142.35078Himonas, A. Alexandrou; Misiołek, Gerard; Ponce, Gustavo; Zhou, Yong 150 2007 Global, small amplitude solutions to nonlinear evolution equations. Zbl 0509.35009Klainerman, S.; Ponce, Gustavo 123 1983 Small solutions to nonlinear Schrödinger equations. Zbl 0786.35121Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 113 1993 Introduction to nonlinear dispersive equations. Zbl 1178.35004Linares, Felipe; Ponce, Gustavo 91 2009 Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations. Zbl 0928.35158Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 79 1998 On the global well-posedness of the Benjamin-Ono equation. Zbl 0732.35038Ponce, Gustavo 75 1991 On the (generalized) Korteweg-de Vries equation. Zbl 0795.35105Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 71 1989 Introduction to nonlinear dispersive equations. 2nd ed. Zbl 1310.35002Linares, Felipe; Ponce, Gustavo 69 2015 Quadratic forms for the 1-D semilinear Schrödinger equation. Zbl 0862.35111Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 63 1996 Global stability of large solutions to the 3D Navier-Stokes equations. Zbl 0795.35082Ponce, G.; Racke, R.; Sideris, T. C.; Titi, E. S. 62 1994 Higher-order nonlinear dispersive equations. Zbl 0810.35122Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 53 1994 The Cauchy problem for quasi-linear Schrödinger equations. Zbl 1177.35221Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 51 2004 On the Zakharov and Zakharov-Schulman systems. Zbl 0823.35158Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 50 1995 On uniqueness properties of solutions of the \(k\)-generalized KdV equations. Zbl 1122.35124Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 48 2007 Remarks on a paper by J. T. Beale, T. Kato, and A. Majda (Remarks on the breakdown of smooth solutions for the 3-dimensional Euler equations). Zbl 0589.76040Ponce, Gustavo 43 1985 Interaction equations for short and long dispersive waves. Zbl 0909.35123Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 42 1998 Lax pairs and higher order models for water waves. Zbl 0796.35148Ponce, Gustavo 40 1993 On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations. Zbl 0855.35112Birnir, Björn; Kenig, Carlos E.; Ponce, Gustavo; Svanstedt, Nils; Vega, Luis 40 1996 On uniqueness properties of solutions of Schrödinger equations. Zbl 1124.35068Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 39 2006 Local regularity of nonlinear wave equations in three space dimensions. Zbl 0803.35096Ponce, Gustavo; Sideris, Thomas C. 39 1993 On the generalized Benjamin-Ono equation. Zbl 0804.35105Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 36 1994 On unique continuation for nonlinear Schrödinger equations. Zbl 1041.35072Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 36 2003 Non-uniform continuity in \(H^1\) of the solution map of the CH equation. Zbl 1127.35056Himonas, A. Alexandrou; Misiołek, Gerard; Ponce, Gustavo 34 2007 On the persistent properties of solutions to semi-linear Schrödinger equation. Zbl 1228.35229Nahas, J.; Ponce, G. 34 2009 On the Davey-Stewartson systems. Zbl 0807.35136Linares, Felipe; Ponce, Gustavo 33 1993 Hardy’s uncertainty principle, convexity and Schrödinger evolutions. Zbl 1158.35018Escauriaza, Luis; Kenig, Carlos E.; Ponce, G.; Vega, Luis 32 2008 The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. Zbl 1205.35249Fonseca, Germán; Ponce, Gustavo 31 2011 Well-posedness of the Euler and Navier-Stokes equations in the Lebesgue spaces \(L^ p_ s({\mathbb{R}}^ 2)\). Zbl 0615.35078Kato, Tosio; Ponce, Gustavo 30 1987 The sharp Hardy uncertainty principle for Schrödinger evolutions. Zbl 1220.35008Escauriaza, Luis; Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 30 2010 On the support of solutions to the generalized KdV equation. Zbl 1001.35106Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 28 2002 A model system for strong interaction between internal solitary waves. Zbl 0752.35056Bona, Jerry L.; Ponce, Gustavo; Saut, Jean-Claude; Tom, Michael M. 27 1992 On the decay properties of solutions to a class of Schrödinger equations. Zbl 1185.35252Dawson, L.; McGahagan, H.; Ponce, G. 25 2008 Global well-posedness for semilinear wave equations. Zbl 0961.35092Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 24 2000 Dispersive blow-up for nonlinear Schrödinger equations revisited. Zbl 1304.35132Bona, J. L.; Ponce, G.; Saut, J.-C.; Sparber, C. 23 2014 The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. II. Zbl 1235.35243Fonseca, Germán; Linares, Felipe; Ponce, Gustavo 22 2012 The Hardy uncertainty principle revisited. Zbl 1242.35017Cowling, M.; Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 22 2010 Extension and representation of divergence-free vector fields on bounded domains. Zbl 0980.53022Kato, Tosio; Mitrea, Marius; Ponce, Gustavo; Taylor, Michael 22 2000 Nonlinear small data scattering for the generalized Korteweg-de Vries equation. Zbl 0771.35062Ponce, Gustavo; Vega, Luis 21 1990 Uniqueness properties of solutions to Schrödinger equations. Zbl 1268.35112Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 21 2012 Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions. Zbl 0884.35138Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 21 1997 Convexity properties of solutions to the free Schrödinger equation with Gaussian decay. Zbl 1169.35307Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 21 2008 On the concentration of blow up solutions for the generalized KdV equation critical in \(L^2\). Zbl 0970.35125Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 21 2000 Regularity of solutions to nonlinear dispersive equations. Zbl 0699.35036Ponce, Gustavo 20 1989 Global well-posedness for the modified Korteweg-de Vries equation. Zbl 0930.35154Fonseca, German; Linares, Felipe; Ponce, Gustavo 20 1999 The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces. Zbl 06295441Fonseca, Germán; Linares, Felipe; Ponce, Gustavo 20 2013 On the unique continuation of solutions to the generalized KdV equation. Zbl 1055.35102Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 19 2003 On the propagation of regularity and decay of solutions to the \(k\)-generalized Korteweg-de Vries equation. Zbl 1326.35317Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 17 2015 Variable coefficient Schrödinger flows for ultrahyperbolic operators. Zbl 1088.35065Kenig, C. E.; Ponce, G.; Rolvung, C.; Vega, L. 16 2005 On the hierarchy of the generalized KdV equations. Zbl 0849.35121Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 15 1994 Unique continuation for Schrödinger evolutions, with applications to profiles of concentration and traveling waves. Zbl 1219.35203Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 15 2011 On the well-posedness of Benney’s interaction equation of short and long waves. Zbl 0861.35104Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 14 1996 On the interaction of nearly parallel vortex filaments. Zbl 1073.76014Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 14 2003 Well-posedness for the Benney-Roskes/Zakharov-Rubenchik system. Zbl 1079.35096Ponce, Gustavo; Saut, Jean-Claude 14 2005 On the propagation of regularities in solutions of the Benjamin-Ono equation. Zbl 1329.35268Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 14 2016 Uncertainty principle of Morgan type and Schrödinger evolutions. Zbl 1228.35223Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 13 2011 On nonstationary flows of viscous and ideal fluids in \(L^ p_ s({\mathbb{R}}^ 2)\). Zbl 0649.76011Kato, Tosio; Ponce, Gustavo 13 1987 Global existence for the critical generalized KdV equation. Zbl 1034.35121Fonseca, G.; Linares, F.; Ponce, G. 12 2003 On the IVP for the nonlinear Schrödinger equations. Zbl 0846.35128Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 12 1995 The local ill-posedness of the modified KdV equation. Zbl 0858.35130Birnir, Björn; Ponce, Gustavo; Svanstedt, Nils 12 1996 The Navier-Stokes equation with weak initial data. Zbl 0837.35116Kato, Tosio; Ponce, Gustavo 11 1994 On the persistence properties of solutions of nonlinear dispersive equations in weighted Sobolev spaces. Zbl 1236.35169Nahas, J.; Ponce, G. 11 2011 Uniqueness properties of solutions to the Benjamin-Ono equation and related models. Zbl 1433.35339Kenig, C. E.; Ponce, G.; Vega, L. 11 2020 Decay properties for solutions of fifth order nonlinear dispersive equations. Zbl 1303.35091Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 11 2015 On persistence properties in fractional weighted spaces. Zbl 1328.35198Fonseca, G.; Linares, F.; Ponce, G. 11 2015 Breathers and the dynamics of solutions in KdV type equations. Zbl 1427.76044Muñoz, Claudio; Ponce, Gustavo 11 2019 On decay properties of solutions of the \(k\)-generalized KdV equation. Zbl 1284.35373Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 9 2013 Well-posedness for a higher-order Benjamin-Ono equation. Zbl 1205.35261Linares, Felipe; Pilod, Didier; Ponce, Gustavo 9 2011 On the propagation of regularity of solutions of the Kadomtsev-Petviashvili equation. Zbl 1346.35181Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 9 2016 Decay at infinity of caloric functions within characteristic hyperplanes. Zbl 1116.35018Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 8 2006 Global existence of small solutions to the initial value problem for nonlinear thermoelasticity. Zbl 0725.35065Ponce, Gustavo; Racke, Reinhard 8 1990 On the regularity of solutions to a class of nonlinear dispersive equations. Zbl 1375.35452Linares, Felipe; Ponce, Gustavo; Smith, Derek L. 8 2017 The general quasilinear ultrahyperbolic Schrödinger equation. Zbl 1122.35137Kenig, Carlos E.; Ponce, Gustavo; Rolvung, Christian; Vega, Luis 7 2006 Hardy uncertainty principle, convexity and parabolic evolutions. Zbl 1356.35045Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 7 2016 On special regularity properties of solutions of the Zakharov-Kuznetsov equation. Zbl 1397.35259Linares, Felipe; Ponce, Gustavo 7 2018 On the asymptotic behavior of solutions to the Benjamin-Ono equation. Zbl 1428.37069Muñoz, Claudio; Ponce, Gustavo 7 2019 Global solutions for the KdV equation with unbounded data. Zbl 0886.35133Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 6 1997 On the initial value problem for the Ishimori system. Zbl 1021.35105Kenig, C. E.; Ponce, Gustavo; Vega, Luis 6 2000 Smoothing properties of solutions to the Benjamin-Ono equation. Zbl 0704.35058Ponce, Gustavo 5 1990 On the Cauchy problem for linear Schrödinger systems with variable coefficient lower order terms. Zbl 0908.35026Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 5 1997 On a class of solutions to the generalized derivative Schrödinger equations. II. Zbl 1428.35524Linares, F.; Ponce, G.; Santos, G. N. 5 2019 A theorem of Paley-Wiener type for Schrödinger evolutions. (Un théorème de type Paley-Wiener pour les évolutions de Schrödinger.) Zbl 1308.35274Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 5 2014 On the regularity of solutions to the \(k\)-generalized Korteweg-de Vries equation. Zbl 1394.35420Kenig, C. E.; Linares, F.; Ponce, G.; Vega, L. 5 2018 On the initial value problem for the one dimensional quasi-linear Schrödinger equations. Zbl 1013.35076Lim, Wee Keong; Ponce, Gustavo 4 2002 On a degenerate Zakharov system. Zbl 1070.35087Linares, F.; Ponce, G.; Saut, J.-C. 4 2005 On a class of solutions to the generalized derivative Schrödinger equations. Zbl 1420.35365Linares, Felipe; Ponce, Gustavo; Santos, Gleison N. 4 2019 Unique continuation properties for solutions to the Camassa-Holm equation and related models. Zbl 1446.35162Linares, Felipe; Ponce, Gustavo 4 2020 Lower bounds for non-trivial travelling wave solutions of equations of KdV type. Zbl 1248.35185Kenig, C. E.; Ponce, G.; Vega, L. 3 2012 On two dimensional incompressible fluids. Zbl 0594.35077Ponce, Gustavo 3 1986 The non-linear Schrödinger equation with a periodic \(\delta\)-interaction. Zbl 1274.76175Pava, Jaime Angulo; Ponce, Gustavo 3 2013 The initial value problem for a class of nonlinear dispersive equations. Zbl 0719.35086Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 3 1990 On a class of solutions to the generalized KdV type equation. Zbl 1428.35456Linares, Felipe; Miyazaki, Hayato; Ponce, Gustavo 3 2019 Properties of solutions to the Camassa-Holm equation on the line in a class containing the peakons. Zbl 1435.35330Linares, Felipe; Ponce, Gustavo; Sideris, Thomas C. 3 2019 On the long time behavior of solutions to the intermediate long wave equation. Zbl 1475.37079Muñoz, Claudio; Ponce, Gustavo; Saut, Jean-Claude 3 2021 Asymptotic behavior of solutions of the dispersion generalized Benjamin-Ono equation. Zbl 1484.35329Linares, F.; Mendez, A.; Ponce, G. 2 2021 Uniqueness properties of solutions to the Benjamin-Ono equation and related models. Zbl 1433.35339Kenig, C. E.; Ponce, G.; Vega, L. 11 2020 Unique continuation properties for solutions to the Camassa-Holm equation and related models. Zbl 1446.35162Linares, Felipe; Ponce, Gustavo 4 2020 On the unique continuation of solutions to non-local non-linear dispersive equations. Zbl 1451.35164Kenig, C. E.; Pilod, D.; Ponce, G.; Vega, L. 1 2020 Breathers and the dynamics of solutions in KdV type equations. Zbl 1427.76044Muñoz, Claudio; Ponce, Gustavo 11 2019 On the asymptotic behavior of solutions to the Benjamin-Ono equation. Zbl 1428.37069Muñoz, Claudio; Ponce, Gustavo 7 2019 On a class of solutions to the generalized derivative Schrödinger equations. II. Zbl 1428.35524Linares, F.; Ponce, G.; Santos, G. N. 5 2019 On a class of solutions to the generalized derivative Schrödinger equations. Zbl 1420.35365Linares, Felipe; Ponce, Gustavo; Santos, Gleison N. 4 2019 On a class of solutions to the generalized KdV type equation. Zbl 1428.35456Linares, Felipe; Miyazaki, Hayato; Ponce, Gustavo 3 2019 Properties of solutions to the Camassa-Holm equation on the line in a class containing the peakons. Zbl 1435.35330Linares, Felipe; Ponce, Gustavo; Sideris, Thomas C. 3 2019 On special regularity properties of solutions of the Zakharov-Kuznetsov equation. Zbl 1397.35259Linares, Felipe; Ponce, Gustavo 7 2018 On the regularity of solutions to the \(k\)-generalized Korteweg-de Vries equation. Zbl 1394.35420Kenig, C. E.; Linares, F.; Ponce, G.; Vega, L. 5 2018 On the regularity of solutions to a class of nonlinear dispersive equations. Zbl 1375.35452Linares, Felipe; Ponce, Gustavo; Smith, Derek L. 8 2017 On the propagation of regularities in solutions of the Benjamin-Ono equation. Zbl 1329.35268Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 14 2016 On the propagation of regularity of solutions of the Kadomtsev-Petviashvili equation. Zbl 1346.35181Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 9 2016 Hardy uncertainty principle, convexity and parabolic evolutions. Zbl 1356.35045Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 7 2016 On the IVP for the \(k\)-generalized Benjamin-Ono equation. Zbl 1403.35087Ponce, Gustavo 2 2016 Proceedings of the XV international conference on hyperbolic problems: theory, numerics, applications. Zbl 1354.00090 1 2016 Introduction to nonlinear dispersive equations. 2nd ed. Zbl 1310.35002Linares, Felipe; Ponce, Gustavo 69 2015 On the propagation of regularity and decay of solutions to the \(k\)-generalized Korteweg-de Vries equation. Zbl 1326.35317Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 17 2015 Decay properties for solutions of fifth order nonlinear dispersive equations. Zbl 1303.35091Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 11 2015 On persistence properties in fractional weighted spaces. Zbl 1328.35198Fonseca, G.; Linares, F.; Ponce, G. 11 2015 Dispersive blow-up for nonlinear Schrödinger equations revisited. Zbl 1304.35132Bona, J. L.; Ponce, G.; Saut, J.-C.; Sparber, C. 23 2014 A theorem of Paley-Wiener type for Schrödinger evolutions. (Un théorème de type Paley-Wiener pour les évolutions de Schrödinger.) Zbl 1308.35274Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 5 2014 The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces. Zbl 06295441Fonseca, Germán; Linares, Felipe; Ponce, Gustavo 20 2013 On decay properties of solutions of the \(k\)-generalized KdV equation. Zbl 1284.35373Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 9 2013 The non-linear Schrödinger equation with a periodic \(\delta\)-interaction. Zbl 1274.76175Pava, Jaime Angulo; Ponce, Gustavo 3 2013 The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. II. Zbl 1235.35243Fonseca, Germán; Linares, Felipe; Ponce, Gustavo 22 2012 Uniqueness properties of solutions to Schrödinger equations. Zbl 1268.35112Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 21 2012 Lower bounds for non-trivial travelling wave solutions of equations of KdV type. Zbl 1248.35185Kenig, C. E.; Ponce, G.; Vega, L. 3 2012 The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. Zbl 1205.35249Fonseca, Germán; Ponce, Gustavo 31 2011 Unique continuation for Schrödinger evolutions, with applications to profiles of concentration and traveling waves. Zbl 1219.35203Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 15 2011 Uncertainty principle of Morgan type and Schrödinger evolutions. Zbl 1228.35223Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 13 2011 On the persistence properties of solutions of nonlinear dispersive equations in weighted Sobolev spaces. Zbl 1236.35169Nahas, J.; Ponce, G. 11 2011 Well-posedness for a higher-order Benjamin-Ono equation. Zbl 1205.35261Linares, Felipe; Pilod, Didier; Ponce, Gustavo 9 2011 The sharp Hardy uncertainty principle for Schrödinger evolutions. Zbl 1220.35008Escauriaza, Luis; Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 30 2010 The Hardy uncertainty principle revisited. Zbl 1242.35017Cowling, M.; Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 22 2010 Introduction to nonlinear dispersive equations. Zbl 1178.35004Linares, Felipe; Ponce, Gustavo 91 2009 On the persistent properties of solutions to semi-linear Schrödinger equation. Zbl 1228.35229Nahas, J.; Ponce, G. 34 2009 Hardy’s uncertainty principle, convexity and Schrödinger evolutions. Zbl 1158.35018Escauriaza, Luis; Kenig, Carlos E.; Ponce, G.; Vega, Luis 32 2008 On the decay properties of solutions to a class of Schrödinger equations. Zbl 1185.35252Dawson, L.; McGahagan, H.; Ponce, G. 25 2008 Convexity properties of solutions to the free Schrödinger equation with Gaussian decay. Zbl 1169.35307Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 21 2008 Persistence properties and unique continuation of solutions of the Camassa-Holm equation. Zbl 1142.35078Himonas, A. Alexandrou; Misiołek, Gerard; Ponce, Gustavo; Zhou, Yong 150 2007 On uniqueness properties of solutions of the \(k\)-generalized KdV equations. Zbl 1122.35124Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 48 2007 Non-uniform continuity in \(H^1\) of the solution map of the CH equation. Zbl 1127.35056Himonas, A. Alexandrou; Misiołek, Gerard; Ponce, Gustavo 34 2007 The initial value problem for the general quasi-linear Schrödinger equation. Zbl 1137.35069Kenig, C. E.; Ponce, G.; Vega, L. 1 2007 On uniqueness properties of solutions of Schrödinger equations. Zbl 1124.35068Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 39 2006 Decay at infinity of caloric functions within characteristic hyperplanes. Zbl 1116.35018Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 8 2006 The general quasilinear ultrahyperbolic Schrödinger equation. Zbl 1122.35137Kenig, Carlos E.; Ponce, Gustavo; Rolvung, Christian; Vega, Luis 7 2006 On the stability of nearly parallel vortex filaments. Zbl 1102.76012Ponce, Gustavo 1 2006 Variable coefficient Schrödinger flows for ultrahyperbolic operators. Zbl 1088.35065Kenig, C. E.; Ponce, G.; Rolvung, C.; Vega, L. 16 2005 Well-posedness for the Benney-Roskes/Zakharov-Rubenchik system. Zbl 1079.35096Ponce, Gustavo; Saut, Jean-Claude 14 2005 On a degenerate Zakharov system. Zbl 1070.35087Linares, F.; Ponce, G.; Saut, J.-C. 4 2005 The Cauchy problem for quasi-linear Schrödinger equations. Zbl 1177.35221Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 51 2004 On unique continuation for nonlinear Schrödinger equations. Zbl 1041.35072Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 36 2003 On the unique continuation of solutions to the generalized KdV equation. Zbl 1055.35102Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 19 2003 On the interaction of nearly parallel vortex filaments. Zbl 1073.76014Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 14 2003 Global existence for the critical generalized KdV equation. Zbl 1034.35121Fonseca, G.; Linares, F.; Ponce, G. 12 2003 On the uniqueness of solutions of higher order nonlinear dispersive equations. Zbl 1050.35100Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 2 2003 On the support of solutions to the generalized KdV equation. Zbl 1001.35106Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 28 2002 On the initial value problem for the one dimensional quasi-linear Schrödinger equations. Zbl 1013.35076Lim, Wee Keong; Ponce, Gustavo 4 2002 On the ill-posedness of some canonical dispersive equations. Zbl 1034.35145Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 160 2001 Global well-posedness for semilinear wave equations. Zbl 0961.35092Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 24 2000 Extension and representation of divergence-free vector fields on bounded domains. Zbl 0980.53022Kato, Tosio; Mitrea, Marius; Ponce, Gustavo; Taylor, Michael 22 2000 On the concentration of blow up solutions for the generalized KdV equation critical in \(L^2\). Zbl 0970.35125Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 21 2000 On the initial value problem for the Ishimori system. Zbl 1021.35105Kenig, C. E.; Ponce, Gustavo; Vega, Luis 6 2000 Tosio Kato (1917–1999). Zbl 1036.01507Cordes, Heinz; Jensen, Arne; Kuroda, S. T.; Ponce, Gustavo; Simon, Barry 1 2000 Global well-posedness for the modified Korteweg-de Vries equation. Zbl 0930.35154Fonseca, German; Linares, Felipe; Ponce, Gustavo 20 1999 Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations. Zbl 0928.35158Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 79 1998 Interaction equations for short and long dispersive waves. Zbl 0909.35123Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 42 1998 On nonlinear dispersive equations. Zbl 0920.35138Ponce, Gustavo 1 1998 Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions. Zbl 0884.35138Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 21 1997 Global solutions for the KdV equation with unbounded data. Zbl 0886.35133Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 6 1997 On the Cauchy problem for linear Schrödinger systems with variable coefficient lower order terms. Zbl 0908.35026Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 5 1997 On the smoothing properties of some dispersive hyperbolic systems. Zbl 0887.35027Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 1 1997 On the well posedness of some nonlinear evolution equations. Zbl 0899.35042Ponce, Gustavo 1 1997 A bilinear estimate with applications to the KdV equation. Zbl 0848.35114Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 343 1996 Quadratic forms for the 1-D semilinear Schrödinger equation. Zbl 0862.35111Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 63 1996 On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations. Zbl 0855.35112Birnir, Björn; Kenig, Carlos E.; Ponce, Gustavo; Svanstedt, Nils; Vega, Luis 40 1996 On the well-posedness of Benney’s interaction equation of short and long waves. Zbl 0861.35104Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 14 1996 The local ill-posedness of the modified KdV equation. Zbl 0858.35130Birnir, Björn; Ponce, Gustavo; Svanstedt, Nils 12 1996 On the Zakharov and Zakharov-Schulman systems. Zbl 0823.35158Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 50 1995 On the IVP for the nonlinear Schrödinger equations. Zbl 0846.35128Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 12 1995 Global stability of large solutions to the 3D Navier-Stokes equations. Zbl 0795.35082Ponce, G.; Racke, R.; Sideris, T. C.; Titi, E. S. 62 1994 Higher-order nonlinear dispersive equations. Zbl 0810.35122Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 53 1994 On the generalized Benjamin-Ono equation. Zbl 0804.35105Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 36 1994 On the hierarchy of the generalized KdV equations. Zbl 0849.35121Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 15 1994 The Navier-Stokes equation with weak initial data. Zbl 0837.35116Kato, Tosio; Ponce, Gustavo 11 1994 Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Zbl 0808.35128Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 591 1993 The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices. Zbl 0787.35090Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 175 1993 Small solutions to nonlinear Schrödinger equations. Zbl 0786.35121Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 113 1993 Lax pairs and higher order models for water waves. Zbl 0796.35148Ponce, Gustavo 40 1993 Local regularity of nonlinear wave equations in three space dimensions. Zbl 0803.35096Ponce, Gustavo; Sideris, Thomas C. 39 1993 On the Davey-Stewartson systems. Zbl 0807.35136Linares, Felipe; Ponce, Gustavo 33 1993 A model system for strong interaction between internal solitary waves. Zbl 0752.35056Bona, Jerry L.; Ponce, Gustavo; Saut, Jean-Claude; Tom, Michael M. 27 1992 Oscillatory integrals and regularity of dispersive equations. Zbl 0738.35022Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 311 1991 Well-posedness of the initial value problem for the Korteweg-de Vries equation. Zbl 0737.35102Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 293 1991 On the global well-posedness of the Benjamin-Ono equation. Zbl 0732.35038Ponce, Gustavo 75 1991 Nonlinear small data scattering for the generalized Korteweg-de Vries equation. Zbl 0771.35062Ponce, Gustavo; Vega, Luis 21 1990 ...and 13 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,340 Authors 67 Ponce, Gustavo 59 Guo, Boling 51 Kenig, Carlos Eduardo 49 Fan, Jishan 48 Vega, Luis 45 Linares, Felipe 45 Zhou, Yong 41 Himonas, A. Alexandrou 36 Hayashi, Nakao 33 Yin, Zhaoyang 30 Liu, Yue 29 Li, Yongsheng 29 Yan, Wei 29 Zhu, Mingxuan 28 Ozawa, Tohru 27 Naumkin, Pavel Ivanovich 26 Zhang, Bingyu 23 Guo, Zhengguang 23 Martel, Yvan 23 Saut, Jean-Claude 22 Carvajal, Xavier Paredes 22 Cui, Shangbin 22 Panthee, Mahendra 22 Wang, Baoxiang 21 Esfahani, Amin 21 Molinet, Luc 21 Pastor, Ademir 21 Pu, Xueke 21 Tataru, Daniel 21 Zhou, Shouming 19 Ikehata, Ryo 19 Jiang, Zaihong 19 Muñoz, Claudio 18 Lai, Shaoyong 18 Merle, Frank 18 Mu, Chunlai 18 Tzvetkov, Nikolay 17 Bona, Jerry Lloyd 17 Huo, Zhaohui 17 Lar’kin, Nikolaj Andreevich 17 Wu, Jiahong 16 Guo, Zihua 16 Huang, Jianhua 16 Isaza, Pedro 16 Staffilani, Gigliola 16 Tian, Lixin 16 Wan, Renhui 16 Yamazaki, Kazuo 15 Miao, Changxing 14 Dong, Boqing 14 Farah, Luiz Gustavo 14 Mejía, Jorge 14 Mi, Yongsheng 14 Nakamura, Gen 14 Pilod, Didier 14 Segata, Jun-ichi 14 Yuan, Baoquan 13 Chae, Dongho 13 Oh, Tadahiro 13 Pazoto, Ademir Fernando 13 Selberg, Sigmund 13 Wang, Chengbo 13 Wang, Ming 13 Ye, Zhuan 12 Alejo, Miguel A. 12 Gao, Hongjun 12 Kaikina, Elena Igorevna 12 Liu, Qiao 12 Metcalfe, Jason L. 12 Zhao, Jihong 12 Zhao, Xiaopeng 11 Angulo Pava, Jaime 11 Chen, Wengu 11 Chen, Zhimin 11 Fu, Ying 11 Ma, Caochuan 11 Petronilho, Gerson 11 Sun, Shuming 11 Tao, Terence 11 Tsutsumi, Yoshio 11 Wang, Yuzhao 11 Xu, Xiaojing 10 Banica, Valeria 10 Corcho, Adán J. 10 Hayat, Tasawar 10 Jia, Yueling 10 Jin, Liangbing 10 Kappeler, Thomas 10 Klainerman, Sergiu 10 Kwak, Chulkwang 10 Li, Junfeng 10 Mantzavinos, Dionyssios 10 Ogawa, Takayoshi 10 Scialom, Marcia 10 Yao, Zhengan 9 Al-saedi, Ahmed Eid Salem 9 Bustamante, Eddye 9 Chen, Jiecheng 9 Colliander, James E. 9 Faminskii, Andrei V. ...and 2,240 more Authors all top 5 Cited in 296 Serials 254 Journal of Differential Equations 204 Journal of Mathematical Analysis and Applications 181 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 104 Communications in Partial Differential Equations 97 Journal of Functional Analysis 84 Journal of Mathematical Physics 71 Discrete and Continuous Dynamical Systems 70 Nonlinear Analysis. Real World Applications 63 Communications in Mathematical Physics 52 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 50 SIAM Journal on Mathematical Analysis 49 Communications on Pure and Applied Analysis 48 ZAMP. Zeitschrift für angewandte Mathematik und Physik 47 Transactions of the American Mathematical Society 46 Advances in Mathematics 46 Proceedings of the American Mathematical Society 42 Archive for Rational Mechanics and Analysis 41 Applied Mathematics Letters 39 Journal of Evolution Equations 37 Applicable Analysis 31 Journal of Mathematical Fluid Mechanics 30 Mathematical Methods in the Applied Sciences 30 NoDEA. Nonlinear Differential Equations and Applications 29 Nonlinearity 28 Acta Mathematica Sinica. English Series 27 Duke Mathematical Journal 27 Journal de Mathématiques Pures et Appliquées. Neuvième Série 27 Abstract and Applied Analysis 26 Monatshefte für Mathematik 26 Journal of Nonlinear Science 25 Applied Mathematics and Computation 25 Physica D 25 The Journal of Fourier Analysis and Applications 23 Nonlinear Analysis. Theory, Methods & Applications 22 Journal d’Analyse Mathématique 22 Mathematische Annalen 22 Boundary Value Problems 21 Communications in Contemporary Mathematics 21 Journal of Hyperbolic Differential Equations 19 Journal of Dynamics and Differential Equations 18 Computers & Mathematics with Applications 17 Discrete and Continuous Dynamical Systems. Series B 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 16 Acta Applicandae Mathematicae 16 Calculus of Variations and Partial Differential Equations 14 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 14 Discrete and Continuous Dynamical Systems. Series S 13 Journal of the American Mathematical Society 13 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 12 Revista Matemática Iberoamericana 12 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 12 Journal of Inequalities and Applications 11 Annali di Matematica Pura ed Applicata. Serie Quarta 11 Forum Mathematicum 10 Communications on Pure and Applied Mathematics 10 Applied Mathematics and Optimization 10 Quarterly of Applied Mathematics 10 Acta Mathematicae Applicatae Sinica. English Series 10 Séminaire Laurent Schwartz. EDP et Applications 9 Mathematische Zeitschrift 9 Chinese Annals of Mathematics. Series B 9 Bulletin of the Brazilian Mathematical Society. New Series 9 Advances in Mathematical Physics 9 Science China. Mathematics 8 Annales de l’Institut Fourier 8 Inventiones Mathematicae 8 Mathematische Nachrichten 8 Zeitschrift für Analysis und ihre Anwendungen 8 The Journal of Geometric Analysis 8 Mathematical Physics, Analysis and Geometry 8 Journal of the European Mathematical Society (JEMS) 8 Journal of Pseudo-Differential Operators and Applications 8 Analysis and Mathematical Physics 8 AIMS Mathematics 7 Acta Mathematica 7 Indiana University Mathematics Journal 7 Osaka Journal of Mathematics 7 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 7 Annals of Mathematics. Second Series 7 Annales Henri Poincaré 7 Journal of Nonlinear Mathematical Physics 6 Letters in Mathematical Physics 6 Journal of Computational and Applied Mathematics 6 Proceedings of the Japan Academy. Series A 6 Publications of the Research Institute for Mathematical Sciences, Kyoto University 6 Geometric and Functional Analysis. GAFA 6 Applied and Computational Harmonic Analysis 6 Electronic Journal of Differential Equations (EJDE) 6 São Paulo Journal of Mathematical Sciences 6 Mathematical Control and Related Fields 5 Journal of Computational Physics 5 Mathematics of Computation 5 Bulletin of the Korean Mathematical Society 5 Asymptotic Analysis 5 Potential Analysis 5 Physics of Fluids 5 Discrete Dynamics in Nature and Society 5 Communications in Nonlinear Science and Numerical Simulation 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 Frontiers of Mathematics in China ...and 196 more Serials all top 5 Cited in 48 Fields 2,902 Partial differential equations (35-XX) 862 Fluid mechanics (76-XX) 277 Dynamical systems and ergodic theory (37-XX) 176 Harmonic analysis on Euclidean spaces (42-XX) 101 Quantum theory (81-XX) 99 Numerical analysis (65-XX) 88 Operator theory (47-XX) 83 Functional analysis (46-XX) 74 Probability theory and stochastic processes (60-XX) 69 Real functions (26-XX) 65 Statistical mechanics, structure of matter (82-XX) 61 Systems theory; control (93-XX) 54 Global analysis, analysis on manifolds (58-XX) 52 Geophysics (86-XX) 45 Mechanics of deformable solids (74-XX) 45 Optics, electromagnetic theory (78-XX) 33 Ordinary differential equations (34-XX) 33 Calculus of variations and optimal control; optimization (49-XX) 23 Differential geometry (53-XX) 20 Biology and other natural sciences (92-XX) 15 Relativity and gravitational theory (83-XX) 14 Abstract harmonic analysis (43-XX) 13 Integral transforms, operational calculus (44-XX) 12 Functions of a complex variable (30-XX) 12 Integral equations (45-XX) 11 Potential theory (31-XX) 10 Topological groups, Lie groups (22-XX) 10 Mechanics of particles and systems (70-XX) 10 Classical thermodynamics, heat transfer (80-XX) 9 Special functions (33-XX) 8 Difference and functional equations (39-XX) 5 Approximations and expansions (41-XX) 4 History and biography (01-XX) 4 Nonassociative rings and algebras (17-XX) 4 Astronomy and astrophysics (85-XX) 3 Mathematical logic and foundations (03-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Computer science (68-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Measure and integration (28-XX) 2 Statistics (62-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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