Edit Profile (opens in new tab) Ponce, Gustavo Co-Author Distance Author ID: ponce.gustavo Published as: Ponce, Gustavo; Ponce, G. Homepage: http://www.math.ucsb.edu/~ponce/ External Links: MGP · Wikidata · ResearchGate · GND · IdRef Documents Indexed: 126 Publications since 1983, including 2 Books and 4 Additional arXiv Preprints 4 Contributions as Editor Biographic References: 1 Publication Co-Authors: 49 Co-Authors with 110 Joint Publications 1,499 Co-Co-Authors all top 5 Co-Authors 20 single-authored 52 Vega, Luis 49 Kenig, Carlos Eduardo 31 Linares, Felipe 12 Escauriaza Zubiria, Luis 7 Fonseca, Germán Eduardo 5 Isaza, Pedro 5 Kato, Tosio 5 Saut, Jean-Claude 4 Muñoz, Claudio 3 Bekiranov, Daniella 3 Bona, Jerry Lloyd 3 Ogawa, Takayoshi 3 Sideris, Thomas C. 2 Angulo Pava, Jaime 2 Birnir, Bjorn 2 Dafermos, Constantine 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 Freire, Ricardo. C. 1 Hoàng Xuân Phù 1 Holden, Helge 1 Hong, Christian 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 Vietnam Journal of Mathematics 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 127 Partial differential equations (35-XX) 23 Fluid mechanics (76-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 Functional analysis (46-XX) 4 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Operator theory (47-XX) 2 Numerical analysis (65-XX) 2 Optics, electromagnetic theory (78-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 6,285 times in 3,625 Documents Cited by ▼ Year ▼ Commutator estimates and the Euler and Navier-Stokes equations. Zbl 0671.35066 Kato, Tosio; Ponce, Gustavo 999 1988 Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Zbl 0808.35128 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 677 1993 A bilinear estimate with applications to the KdV equation. Zbl 0848.35114 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 386 1996 Oscillatory integrals and regularity of dispersive equations. Zbl 0738.35022 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 363 1991 Well-posedness of the initial value problem for the Korteweg-de Vries equation. Zbl 0737.35102 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 352 1991 Global existence of small solutions to a class of nonlinear evolution equations. Zbl 0576.35023 Ponce, Gustavo 195 1985 The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices. Zbl 0787.35090 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 193 1993 On the ill-posedness of some canonical dispersive equations. Zbl 1034.35145 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 186 2001 Persistence properties and unique continuation of solutions of the Camassa-Holm equation. Zbl 1142.35078 Himonas, A. Alexandrou; Misiołek, Gerard; Ponce, Gustavo; Zhou, Yong 172 2007 Global, small amplitude solutions to nonlinear evolution equations. Zbl 0509.35009 Klainerman, S.; Ponce, Gustavo 133 1983 Small solutions to nonlinear Schrödinger equations. Zbl 0786.35121 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 124 1993 Introduction to nonlinear dispersive equations. Zbl 1178.35004 Linares, Felipe; Ponce, Gustavo 118 2009 Introduction to nonlinear dispersive equations. 2nd ed. Zbl 1310.35002 Linares, Felipe; Ponce, Gustavo 103 2015 Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations. Zbl 0928.35158 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 90 1998 On the global well-posedness of the Benjamin-Ono equation. Zbl 0732.35038 Ponce, Gustavo 83 1991 On the (generalized) Korteweg-de Vries equation. Zbl 0795.35105 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 83 1989 Global stability of large solutions to the 3D Navier-Stokes equations. Zbl 0795.35082 Ponce, G.; Racke, R.; Sideris, T. C.; Titi, E. S. 71 1994 Quadratic forms for the 1-D semilinear Schrödinger equation. Zbl 0862.35111 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 69 1996 The Cauchy problem for quasi-linear Schrödinger equations. Zbl 1177.35221 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 63 2004 On the Zakharov and Zakharov-Schulman systems. Zbl 0823.35158 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 58 1995 Higher-order nonlinear dispersive equations. Zbl 0810.35122 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 57 1994 On uniqueness properties of solutions of the \(k\)-generalized KdV equations. Zbl 1122.35124 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 55 2007 Interaction equations for short and long dispersive waves. Zbl 0909.35123 Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 49 1998 On the persistent properties of solutions to semi-linear Schrödinger equation. Zbl 1228.35229 Nahas, J.; Ponce, G. 46 2009 On uniqueness properties of solutions of Schrödinger equations. Zbl 1124.35068 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 46 2006 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 0589.76040 Ponce, Gustavo 45 1985 Lax pairs and higher order models for water waves. Zbl 0796.35148 Ponce, Gustavo 44 1993 Non-uniform continuity in \(H^1\) of the solution map of the CH equation. Zbl 1127.35056 Himonas, A. Alexandrou; Misiołek, Gerard; Ponce, Gustavo 43 2007 On the generalized Benjamin-Ono equation. Zbl 0804.35105 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 42 1994 On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations. Zbl 0855.35112 Birnir, Björn; Kenig, Carlos E.; Ponce, Gustavo; Svanstedt, Nils; Vega, Luis 41 1996 Local regularity of nonlinear wave equations in three space dimensions. Zbl 0803.35096 Ponce, Gustavo; Sideris, Thomas C. 41 1993 On the Davey-Stewartson systems. Zbl 0807.35136 Linares, Felipe; Ponce, Gustavo 40 1993 The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. Zbl 1205.35249 Fonseca, Germán; Ponce, Gustavo 40 2011 The sharp Hardy uncertainty principle for Schrödinger evolutions. Zbl 1220.35008 Escauriaza, Luis; Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 40 2010 On unique continuation for nonlinear Schrödinger equations. Zbl 1041.35072 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 40 2003 Hardy’s uncertainty principle, convexity and Schrödinger evolutions. Zbl 1158.35018 Escauriaza, Luis; Kenig, Carlos E.; Ponce, G.; Vega, Luis 39 2008 Well-posedness of the Euler and Navier-Stokes equations in the Lebesgue spaces \(L^ p_ s({\mathbb{R}}^ 2)\). Zbl 0615.35078 Kato, Tosio; Ponce, Gustavo 36 1987 A model system for strong interaction between internal solitary waves. Zbl 0752.35056 Bona, Jerry L.; Ponce, Gustavo; Saut, Jean-Claude; Tom, Michael M. 33 1992 On the decay properties of solutions to a class of Schrödinger equations. Zbl 1185.35252 Dawson, L.; McGahagan, H.; Ponce, G. 32 2008 Dispersive blow-up for nonlinear Schrödinger equations revisited. Zbl 1304.35132 Bona, J. L.; Ponce, G.; Saut, J.-C.; Sparber, C. 31 2014 On the support of solutions to the generalized KdV equation. Zbl 1001.35106 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 30 2002 Global well-posedness for semilinear wave equations. Zbl 0961.35092 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 29 2000 Extension and representation of divergence-free vector fields on bounded domains. Zbl 0980.53022 Kato, Tosio; Mitrea, Marius; Ponce, Gustavo; Taylor, Michael 29 2000 The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces. Zbl 1511.35035 Fonseca, Germán; Linares, Felipe; Ponce, Gustavo 28 2013 Uniqueness properties of solutions to Schrödinger equations. Zbl 1268.35112 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 28 2012 On the propagation of regularity and decay of solutions to the \(k\)-generalized Korteweg-de Vries equation. Zbl 1326.35317 Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 27 2015 The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. II. Zbl 1235.35243 Fonseca, Germán; Linares, Felipe; Ponce, Gustavo 27 2012 Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions. Zbl 0884.35138 Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 25 1997 The Hardy uncertainty principle revisited. Zbl 1242.35017 Cowling, M.; Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 25 2010 Global well-posedness for the modified Korteweg-de Vries equation. Zbl 0930.35154 Fonseca, German; Linares, Felipe; Ponce, Gustavo 24 1999 On the concentration of blow up solutions for the generalized KdV equation critical in \(L^2\). Zbl 0970.35125 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 23 2000 Convexity properties of solutions to the free Schrödinger equation with Gaussian decay. Zbl 1169.35307 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 23 2008 On the propagation of regularities in solutions of the Benjamin-Ono equation. Zbl 1329.35268 Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 22 2016 Regularity of solutions to nonlinear dispersive equations. Zbl 0699.35036 Ponce, Gustavo 22 1989 Nonlinear small data scattering for the generalized Korteweg-de Vries equation. Zbl 0771.35062 Ponce, Gustavo; Vega, Luis 21 1990 On the unique continuation of solutions to the generalized KdV equation. Zbl 1055.35102 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 20 2003 Well-posedness for the Benney-Roskes/Zakharov-Rubenchik system. Zbl 1079.35096 Ponce, Gustavo; Saut, Jean-Claude 19 2005 Variable coefficient Schrödinger flows for ultrahyperbolic operators. Zbl 1088.35065 Kenig, C. E.; Ponce, G.; Rolvung, C.; Vega, L. 18 2005 Unique continuation properties for solutions to the Camassa-Holm equation and related models. Zbl 1446.35162 Linares, Felipe; Ponce, Gustavo 18 2020 On the well-posedness of Benney’s interaction equation of short and long waves. Zbl 0861.35104 Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 17 1996 Breathers and the dynamics of solutions in KdV type equations. Zbl 1427.76044 Muñoz, Claudio; Ponce, Gustavo 17 2019 On the hierarchy of the generalized KdV equations. Zbl 0849.35121 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 17 1994 On the interaction of nearly parallel vortex filaments. Zbl 1073.76014 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 17 2003 Uniqueness properties of solutions to the Benjamin-Ono equation and related models. Zbl 1433.35339 Kenig, C. E.; Ponce, G.; Vega, L. 17 2020 On special regularity properties of solutions of the Zakharov-Kuznetsov equation. Zbl 1397.35259 Linares, Felipe; Ponce, Gustavo 16 2018 On the regularity of solutions to a class of nonlinear dispersive equations. Zbl 1375.35452 Linares, Felipe; Ponce, Gustavo; Smith, Derek L. 16 2017 On nonstationary flows of viscous and ideal fluids in \(L^ p_ s({\mathbb{R}}^ 2)\). Zbl 0649.76011 Kato, Tosio; Ponce, Gustavo 16 1987 On decay properties of solutions of the \(k\)-generalized KdV equation. Zbl 1284.35373 Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 16 2013 On persistence properties in fractional weighted spaces. Zbl 1328.35198 Fonseca, G.; Linares, F.; Ponce, G. 15 2015 Unique continuation for Schrödinger evolutions, with applications to profiles of concentration and traveling waves. Zbl 1219.35203 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 15 2011 On the propagation of regularity of solutions of the Kadomtsev-Petviashvili equation. Zbl 1346.35181 Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 15 2016 Decay properties for solutions of fifth order nonlinear dispersive equations. Zbl 1303.35091 Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 13 2015 Uncertainty principle of Morgan type and Schrödinger evolutions. Zbl 1228.35223 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 13 2011 Global existence for the critical generalized KdV equation. Zbl 1034.35121 Fonseca, G.; Linares, F.; Ponce, G. 12 2003 The local ill-posedness of the modified KdV equation. Zbl 0858.35130 Birnir, Björn; Ponce, Gustavo; Svanstedt, Nils 12 1996 The Navier-Stokes equation with weak initial data. Zbl 0837.35116 Kato, Tosio; Ponce, Gustavo 12 1994 On the IVP for the nonlinear Schrödinger equations. Zbl 0846.35128 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 12 1995 The general quasilinear ultrahyperbolic Schrödinger equation. Zbl 1122.35137 Kenig, Carlos E.; Ponce, Gustavo; Rolvung, Christian; Vega, Luis 12 2006 On the regularity of solutions to the \(k\)-generalized Korteweg-de Vries equation. Zbl 1394.35420 Kenig, C. E.; Linares, F.; Ponce, G.; Vega, L. 11 2018 Global existence of small solutions to the initial value problem for nonlinear thermoelasticity. Zbl 0725.35065 Ponce, Gustavo; Racke, Reinhard 11 1990 On the persistence properties of solutions of nonlinear dispersive equations in weighted Sobolev spaces. Zbl 1236.35169 Nahas, J.; Ponce, G. 11 2011 Properties of solutions to the Camassa-Holm equation on the line in a class containing the peakons. Zbl 1435.35330 Linares, Felipe; Ponce, Gustavo; Sideris, Thomas C. 11 2019 On a class of solutions to the generalized derivative Schrödinger equations. II. Zbl 1428.35524 Linares, F.; Ponce, G.; Santos, G. N. 10 2019 Well-posedness for a higher-order Benjamin-Ono equation. Zbl 1205.35261 Linares, Felipe; Pilod, Didier; Ponce, Gustavo 10 2011 Decay at infinity of caloric functions within characteristic hyperplanes. Zbl 1116.35018 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 10 2006 On a class of solutions to the generalized derivative Schrödinger equations. Zbl 1420.35365 Linares, Felipe; Ponce, Gustavo; Santos, Gleison N. 9 2019 Hardy uncertainty principle, convexity and parabolic evolutions. Zbl 1356.35045 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 9 2016 On a class of solutions to the generalized KdV type equation. Zbl 1428.35456 Linares, Felipe; Miyazaki, Hayato; Ponce, Gustavo 8 2019 On the initial value problem for the Ishimori system. Zbl 1021.35105 Kenig, C. E.; Ponce, Gustavo; Vega, Luis 7 2000 Global solutions for the KdV equation with unbounded data. Zbl 0886.35133 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 7 1997 On the asymptotic behavior of solutions to the Benjamin-Ono equation. Zbl 1428.37069 Muñoz, Claudio; Ponce, Gustavo 7 2019 Smoothing properties of solutions to the Benjamin-Ono equation. Zbl 0704.35058 Ponce, Gustavo 6 1990 On the Cauchy problem for linear Schrödinger systems with variable coefficient lower order terms. Zbl 0908.35026 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 6 1997 On the unique continuation of solutions to non-local non-linear dispersive equations. Zbl 1451.35164 Kenig, C. E.; Pilod, D.; Ponce, G.; Vega, L. 6 2020 A theorem of Paley-Wiener type for Schrödinger evolutions. (Un théorème de type Paley-Wiener pour les évolutions de Schrödinger.) Zbl 1308.35274 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 5 2014 On a degenerate Zakharov system. Zbl 1070.35087 Linares, F.; Ponce, G.; Saut, J.-C. 5 2005 On the long time behavior of solutions to the intermediate long wave equation. Zbl 1475.37079 Muñoz, Claudio; Ponce, Gustavo; Saut, Jean-Claude 5 2021 On the initial value problem for the one dimensional quasi-linear Schrödinger equations. Zbl 1013.35076 Lim, Wee Keong; Ponce, Gustavo 4 2002 On the IVP for the \(k\)-generalized Benjamin-Ono equation. Zbl 1403.35087 Ponce, Gustavo 4 2016 The non-linear Schrödinger equation with a periodic \(\delta\)-interaction. Zbl 1274.76175 Pava, Jaime Angulo; Ponce, Gustavo 4 2013 On the long time behavior of solutions to the intermediate long wave equation. Zbl 1475.37079 Muñoz, Claudio; Ponce, Gustavo; Saut, Jean-Claude 5 2021 Asymptotic behavior of solutions of the dispersion generalized Benjamin-Ono equation. Zbl 1484.35329 Linares, F.; Mendez, A.; Ponce, G. 2 2021 Unique continuation properties for solutions to the Camassa-Holm equation and related models. Zbl 1446.35162 Linares, Felipe; Ponce, Gustavo 18 2020 Uniqueness properties of solutions to the Benjamin-Ono equation and related models. Zbl 1433.35339 Kenig, C. E.; Ponce, G.; Vega, L. 17 2020 On the unique continuation of solutions to non-local non-linear dispersive equations. Zbl 1451.35164 Kenig, C. E.; Pilod, D.; Ponce, G.; Vega, L. 6 2020 Breathers and the dynamics of solutions in KdV type equations. Zbl 1427.76044 Muñoz, Claudio; Ponce, Gustavo 17 2019 Properties of solutions to the Camassa-Holm equation on the line in a class containing the peakons. Zbl 1435.35330 Linares, Felipe; Ponce, Gustavo; Sideris, Thomas C. 11 2019 On a class of solutions to the generalized derivative Schrödinger equations. II. Zbl 1428.35524 Linares, F.; Ponce, G.; Santos, G. N. 10 2019 On a class of solutions to the generalized derivative Schrödinger equations. Zbl 1420.35365 Linares, Felipe; Ponce, Gustavo; Santos, Gleison N. 9 2019 On a class of solutions to the generalized KdV type equation. Zbl 1428.35456 Linares, Felipe; Miyazaki, Hayato; Ponce, Gustavo 8 2019 On the asymptotic behavior of solutions to the Benjamin-Ono equation. Zbl 1428.37069 Muñoz, Claudio; Ponce, Gustavo 7 2019 On special regularity properties of solutions of the Zakharov-Kuznetsov equation. Zbl 1397.35259 Linares, Felipe; Ponce, Gustavo 16 2018 On the regularity of solutions to the \(k\)-generalized Korteweg-de Vries equation. Zbl 1394.35420 Kenig, C. E.; Linares, F.; Ponce, G.; Vega, L. 11 2018 On the regularity of solutions to a class of nonlinear dispersive equations. Zbl 1375.35452 Linares, Felipe; Ponce, Gustavo; Smith, Derek L. 16 2017 On the propagation of regularities in solutions of the Benjamin-Ono equation. Zbl 1329.35268 Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 22 2016 On the propagation of regularity of solutions of the Kadomtsev-Petviashvili equation. Zbl 1346.35181 Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 15 2016 Hardy uncertainty principle, convexity and parabolic evolutions. Zbl 1356.35045 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 9 2016 On the IVP for the \(k\)-generalized Benjamin-Ono equation. Zbl 1403.35087 Ponce, Gustavo 4 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 1310.35002 Linares, Felipe; Ponce, Gustavo 103 2015 On the propagation of regularity and decay of solutions to the \(k\)-generalized Korteweg-de Vries equation. Zbl 1326.35317 Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 27 2015 On persistence properties in fractional weighted spaces. Zbl 1328.35198 Fonseca, G.; Linares, F.; Ponce, G. 15 2015 Decay properties for solutions of fifth order nonlinear dispersive equations. Zbl 1303.35091 Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 13 2015 Dispersive blow-up for nonlinear Schrödinger equations revisited. Zbl 1304.35132 Bona, J. L.; Ponce, G.; Saut, J.-C.; Sparber, C. 31 2014 A theorem of Paley-Wiener type for Schrödinger evolutions. (Un théorème de type Paley-Wiener pour les évolutions de Schrödinger.) Zbl 1308.35274 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 5 2014 The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces. Zbl 1511.35035 Fonseca, Germán; Linares, Felipe; Ponce, Gustavo 28 2013 On decay properties of solutions of the \(k\)-generalized KdV equation. Zbl 1284.35373 Isaza, Pedro; Linares, Felipe; Ponce, Gustavo 16 2013 The non-linear Schrödinger equation with a periodic \(\delta\)-interaction. Zbl 1274.76175 Pava, Jaime Angulo; Ponce, Gustavo 4 2013 Uniqueness properties of solutions to Schrödinger equations. Zbl 1268.35112 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 28 2012 The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. II. Zbl 1235.35243 Fonseca, Germán; Linares, Felipe; Ponce, Gustavo 27 2012 Lower bounds for non-trivial travelling wave solutions of equations of KdV type. Zbl 1248.35185 Kenig, C. E.; Ponce, G.; Vega, L. 3 2012 The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. Zbl 1205.35249 Fonseca, Germán; Ponce, Gustavo 40 2011 Unique continuation for Schrödinger evolutions, with applications to profiles of concentration and traveling waves. Zbl 1219.35203 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 15 2011 Uncertainty principle of Morgan type and Schrödinger evolutions. Zbl 1228.35223 Escauriaza, 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 1236.35169 Nahas, J.; Ponce, G. 11 2011 Well-posedness for a higher-order Benjamin-Ono equation. Zbl 1205.35261 Linares, Felipe; Pilod, Didier; Ponce, Gustavo 10 2011 The sharp Hardy uncertainty principle for Schrödinger evolutions. Zbl 1220.35008 Escauriaza, Luis; Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 40 2010 The Hardy uncertainty principle revisited. Zbl 1242.35017 Cowling, M.; Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 25 2010 Introduction to nonlinear dispersive equations. Zbl 1178.35004 Linares, Felipe; Ponce, Gustavo 118 2009 On the persistent properties of solutions to semi-linear Schrödinger equation. Zbl 1228.35229 Nahas, J.; Ponce, G. 46 2009 Hardy’s uncertainty principle, convexity and Schrödinger evolutions. Zbl 1158.35018 Escauriaza, Luis; Kenig, Carlos E.; Ponce, G.; Vega, Luis 39 2008 On the decay properties of solutions to a class of Schrödinger equations. Zbl 1185.35252 Dawson, L.; McGahagan, H.; Ponce, G. 32 2008 Convexity properties of solutions to the free Schrödinger equation with Gaussian decay. Zbl 1169.35307 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 23 2008 Persistence properties and unique continuation of solutions of the Camassa-Holm equation. Zbl 1142.35078 Himonas, A. Alexandrou; Misiołek, Gerard; Ponce, Gustavo; Zhou, Yong 172 2007 On uniqueness properties of solutions of the \(k\)-generalized KdV equations. Zbl 1122.35124 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 55 2007 Non-uniform continuity in \(H^1\) of the solution map of the CH equation. Zbl 1127.35056 Himonas, A. Alexandrou; Misiołek, Gerard; Ponce, Gustavo 43 2007 The initial value problem for the general quasi-linear Schrödinger equation. Zbl 1137.35069 Kenig, C. E.; Ponce, G.; Vega, L. 1 2007 On uniqueness properties of solutions of Schrödinger equations. Zbl 1124.35068 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 46 2006 The general quasilinear ultrahyperbolic Schrödinger equation. Zbl 1122.35137 Kenig, Carlos E.; Ponce, Gustavo; Rolvung, Christian; Vega, Luis 12 2006 Decay at infinity of caloric functions within characteristic hyperplanes. Zbl 1116.35018 Escauriaza, L.; Kenig, C. E.; Ponce, G.; Vega, L. 10 2006 On the stability of nearly parallel vortex filaments. Zbl 1102.76012 Ponce, Gustavo 2 2006 Well-posedness for the Benney-Roskes/Zakharov-Rubenchik system. Zbl 1079.35096 Ponce, Gustavo; Saut, Jean-Claude 19 2005 Variable coefficient Schrödinger flows for ultrahyperbolic operators. Zbl 1088.35065 Kenig, C. E.; Ponce, G.; Rolvung, C.; Vega, L. 18 2005 On a degenerate Zakharov system. Zbl 1070.35087 Linares, F.; Ponce, G.; Saut, J.-C. 5 2005 The Cauchy problem for quasi-linear Schrödinger equations. Zbl 1177.35221 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 63 2004 On unique continuation for nonlinear Schrödinger equations. Zbl 1041.35072 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 40 2003 On the unique continuation of solutions to the generalized KdV equation. Zbl 1055.35102 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 20 2003 On the interaction of nearly parallel vortex filaments. Zbl 1073.76014 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 17 2003 Global existence for the critical generalized KdV equation. Zbl 1034.35121 Fonseca, G.; Linares, F.; Ponce, G. 12 2003 On the uniqueness of solutions of higher order nonlinear dispersive equations. Zbl 1050.35100 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 2 2003 On the support of solutions to the generalized KdV equation. Zbl 1001.35106 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 30 2002 On the initial value problem for the one dimensional quasi-linear Schrödinger equations. Zbl 1013.35076 Lim, Wee Keong; Ponce, Gustavo 4 2002 On the ill-posedness of some canonical dispersive equations. Zbl 1034.35145 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 186 2001 Global well-posedness for semilinear wave equations. Zbl 0961.35092 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 29 2000 Extension and representation of divergence-free vector fields on bounded domains. Zbl 0980.53022 Kato, Tosio; Mitrea, Marius; Ponce, Gustavo; Taylor, Michael 29 2000 On the concentration of blow up solutions for the generalized KdV equation critical in \(L^2\). Zbl 0970.35125 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 23 2000 On the initial value problem for the Ishimori system. Zbl 1021.35105 Kenig, C. E.; Ponce, Gustavo; Vega, Luis 7 2000 Tosio Kato (1917–1999). Zbl 1036.01507 Cordes, Heinz; Jensen, Arne; Kuroda, S. T.; Ponce, Gustavo; Simon, Barry 1 2000 Global well-posedness for the modified Korteweg-de Vries equation. Zbl 0930.35154 Fonseca, German; Linares, Felipe; Ponce, Gustavo 24 1999 Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations. Zbl 0928.35158 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 90 1998 Interaction equations for short and long dispersive waves. Zbl 0909.35123 Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 49 1998 On nonlinear dispersive equations. Zbl 0920.35138 Ponce, Gustavo 1 1998 Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions. Zbl 0884.35138 Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 25 1997 Global solutions for the KdV equation with unbounded data. Zbl 0886.35133 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 7 1997 On the Cauchy problem for linear Schrödinger systems with variable coefficient lower order terms. Zbl 0908.35026 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 6 1997 On the smoothing properties of some dispersive hyperbolic systems. Zbl 0887.35027 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 1 1997 On the well posedness of some nonlinear evolution equations. Zbl 0899.35042 Ponce, Gustavo 1 1997 A bilinear estimate with applications to the KdV equation. Zbl 0848.35114 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 386 1996 Quadratic forms for the 1-D semilinear Schrödinger equation. Zbl 0862.35111 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 69 1996 On the ill-posedness of the IVP for the generalized Korteweg-de Vries and nonlinear Schrödinger equations. Zbl 0855.35112 Birnir, Björn; Kenig, Carlos E.; Ponce, Gustavo; Svanstedt, Nils; Vega, Luis 41 1996 On the well-posedness of Benney’s interaction equation of short and long waves. Zbl 0861.35104 Bekiranov, Daniella; Ogawa, Takayoshi; Ponce, Gustavo 17 1996 The local ill-posedness of the modified KdV equation. Zbl 0858.35130 Birnir, Björn; Ponce, Gustavo; Svanstedt, Nils 12 1996 On the Zakharov and Zakharov-Schulman systems. Zbl 0823.35158 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 58 1995 On the IVP for the nonlinear Schrödinger equations. Zbl 0846.35128 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 12 1995 Global stability of large solutions to the 3D Navier-Stokes equations. Zbl 0795.35082 Ponce, G.; Racke, R.; Sideris, T. C.; Titi, E. S. 71 1994 Higher-order nonlinear dispersive equations. Zbl 0810.35122 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 57 1994 On the generalized Benjamin-Ono equation. Zbl 0804.35105 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 42 1994 On the hierarchy of the generalized KdV equations. Zbl 0849.35121 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 17 1994 The Navier-Stokes equation with weak initial data. Zbl 0837.35116 Kato, Tosio; Ponce, Gustavo 12 1994 Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Zbl 0808.35128 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 677 1993 The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices. Zbl 0787.35090 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 193 1993 Small solutions to nonlinear Schrödinger equations. Zbl 0786.35121 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 124 1993 Lax pairs and higher order models for water waves. Zbl 0796.35148 Ponce, Gustavo 44 1993 Local regularity of nonlinear wave equations in three space dimensions. Zbl 0803.35096 Ponce, Gustavo; Sideris, Thomas C. 41 1993 On the Davey-Stewartson systems. Zbl 0807.35136 Linares, Felipe; Ponce, Gustavo 40 1993 A model system for strong interaction between internal solitary waves. Zbl 0752.35056 Bona, Jerry L.; Ponce, Gustavo; Saut, Jean-Claude; Tom, Michael M. 33 1992 Oscillatory integrals and regularity of dispersive equations. Zbl 0738.35022 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 363 1991 Well-posedness of the initial value problem for the Korteweg-de Vries equation. Zbl 0737.35102 Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis 352 1991 On the global well-posedness of the Benjamin-Ono equation. Zbl 0732.35038 Ponce, Gustavo 83 1991 Nonlinear small data scattering for the generalized Korteweg-de Vries equation. Zbl 0771.35062 Ponce, Gustavo; Vega, Luis 21 1990 ...and 13 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,779 Authors 68 Guo, Boling 68 Ponce, Gustavo 54 Kenig, Carlos Eduardo 53 Fan, Jishan 52 Vega, Luis 47 Linares, Felipe 45 Zhou, Yong 44 Himonas, A. Alexandrou 43 Hayashi, Nakao 34 Naumkin, Pavel Ivanovich 34 Yin, Zhaoyang 33 Yan, Wei 32 Liu, Yue 30 Li, Yongsheng 30 Zhang, Bingyu 30 Zhu, Mingxuan 29 Ozawa, Tohru 24 Esfahani, Amin 24 Guo, Zhengguang 24 Wang, Baoxiang 23 Carvajal, Xavier Paredes 23 Cui, Shangbin 23 Lai, Shaoyong 23 Martel, Yvan 23 Panthee, Mahendra 23 Pastor, Ademir 23 Saut, Jean-Claude 22 Pu, Xueke 22 Tataru, Daniel 22 Tzvetkov, Nikolay 22 Zhou, Shouming 21 Ikehata, Ryo 21 Molinet, Luc 20 Jiang, Zaihong 20 Muñoz, Claudio 19 Huo, Zhaohui 18 Bona, Jerry Lloyd 18 Merle, Frank 18 Mu, Chunlai 17 Chae, Dongho 17 Guo, Zihua 17 Huang, Jianhua 17 Lar’kin, Nikolaj Andreevich 17 Nakamura, Gen 17 Staffilani, Gigliola 17 Wan, Renhui 17 Wang, Ming 17 Wu, Jiahong 16 Isaza, Pedro 16 Tian, Lixin 16 Yamazaki, Kazuo 16 Zhao, Xiaopeng 15 Alejo, Miguel A. 15 Farah, Luiz Gustavo 15 Freire, Igor Leite 15 Fu, Ying 15 Mi, Yongsheng 15 Miao, Changxing 15 Oh, Tadahiro 15 Pilod, Didier 15 Segata, Jun-ichi 15 Yao, Zhengan 15 Yu, Yanghai 15 Yuan, Baoquan 14 Dong, Boqing 14 Mejía, Jorge 14 Pazoto, Ademir Fernando 14 Ye, Zhuan 13 Gao, Hongjun 13 Kwak, Chulkwang 13 Selberg, Sigmund 13 Sun, Shuming 13 Wang, Chengbo 13 Zhao, Jihong 12 Angulo Pava, Jaime 12 Banica, Valeria 12 Kaikina, Elena Igorevna 12 Liu, Qiao 12 Ma, Caochuan 12 Metcalfe, Jason L. 12 Petronilho, Gerson 12 Shang, Haifeng 12 Tang, Hao 12 Tsutsumi, Yoshio 11 Cavalcante, Márcio André Araújo 11 Chen, Wengu 11 Chen, Yong 11 Chen, Zhimin 11 Coclite, Giuseppe Maria 11 Corcho, Adán J. 11 Faminskii, Andrei V. 11 Li, Jinlu 11 Nakanishi, Kenji 11 Ogawa, Takayoshi 11 Tao, Terence 11 Wang, Yuzhao 11 Xu, Xiaojing 11 Yan, Fangchi 10 Bustamante, Eddye 10 Di Ruvo, Lorenzo ...and 2,679 more Authors all top 5 Cited in 339 Serials 284 Journal of Differential Equations 227 Journal of Mathematical Analysis and Applications 198 Nonlinear Analysis. 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(English Edition) 11 Bulletin of the Brazilian Mathematical Society. New Series 10 Communications on Pure and Applied Mathematics 10 Applied Mathematics and Optimization 10 Electronic Journal of Differential Equations (EJDE) 10 Annales Henri Poincaré 10 Journal of Nonlinear Mathematical Physics 10 Journal of Pseudo-Differential Operators and Applications 10 Séminaire Laurent Schwartz. EDP et Applications 10 AIMS Mathematics 9 Annales de l’Institut Fourier 9 Studies in Applied Mathematics 9 Zeitschrift für Analysis und ihre Anwendungen 9 Journal of Scientific Computing 9 Mathematical Physics, Analysis and Geometry 9 Communications in Nonlinear Science and Numerical Simulation 9 Advances in Mathematical Physics 8 Inventiones Mathematicae 8 Osaka Journal of Mathematics 8 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 8 São Paulo Journal of Mathematical Sciences 8 Analysis and Mathematical Physics 8 Annals of PDE 7 Acta Mathematica 7 Advances in Differential Equations 7 Annals of Mathematics. Second Series 7 Evolution Equations and Control Theory 6 Letters in Mathematical Physics 6 Journal of Computational and Applied Mathematics 6 Proceedings of the Japan Academy. 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GAFA 6 Potential Analysis ...and 239 more Serials all top 5 Cited in 47 Fields 3,433 Partial differential equations (35-XX) 1,057 Fluid mechanics (76-XX) 343 Dynamical systems and ergodic theory (37-XX) 223 Harmonic analysis on Euclidean spaces (42-XX) 123 Numerical analysis (65-XX) 117 Quantum theory (81-XX) 108 Functional analysis (46-XX) 105 Operator theory (47-XX) 100 Real functions (26-XX) 93 Probability theory and stochastic processes (60-XX) 74 Statistical mechanics, structure of matter (82-XX) 72 Geophysics (86-XX) 69 Systems theory; control (93-XX) 57 Global analysis, analysis on manifolds (58-XX) 57 Mechanics of deformable solids (74-XX) 54 Optics, electromagnetic theory (78-XX) 38 Calculus of variations and optimal control; optimization (49-XX) 37 Ordinary differential equations (34-XX) 30 Differential geometry (53-XX) 26 Biology and other natural sciences (92-XX) 23 Integral transforms, operational calculus (44-XX) 19 Relativity and gravitational theory (83-XX) 17 Functions of a complex variable (30-XX) 17 Classical thermodynamics, heat transfer (80-XX) 16 Abstract harmonic analysis (43-XX) 15 Potential theory (31-XX) 14 Integral equations (45-XX) 13 Difference and functional equations (39-XX) 12 Special functions (33-XX) 12 Mechanics of particles and systems (70-XX) 11 Topological groups, Lie groups (22-XX) 7 Computer science (68-XX) 7 Astronomy and astrophysics (85-XX) 6 Number theory (11-XX) 5 History and biography (01-XX) 5 Approximations and expansions (41-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Nonassociative rings and algebras (17-XX) 4 Measure and integration (28-XX) 3 Mathematical logic and foundations (03-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-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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