Edit Profile Merle, Frank Compute Distance To: Compute Author ID: merle.frank Published as: Merle, F.; Merle, Franck; Merle, Frank Homepage: https://www.ihes.fr/en/professeur/frank-merle-2/ External Links: MGP · Math-Net.Ru · Wikidata · ResearchGate · dblp Documents Indexed: 156 Publications since 1987, including 4 Books all top 5 Co-Authors 26 single-authored 34 Martel, Yvan 25 Raphael, Pierre 22 Kenig, Carlos Eduardo 21 Zaag, Hatem 18 Duyckaerts, Thomas 6 Szeftel, Jérémie 5 Peletier, Lambertus Adrianus 4 Berestycki, Henri 4 Hilhorst, Danielle 4 Mimura, Masayasu 4 Pakdaman, Khashayar 3 Brézis, Haïm 3 Collot, Charles 3 Matano, Hiroshi 3 Rodnianski, Igor 2 Balabane, Mikhael 2 Cazenave, Thierry 2 Côte, Raphaël 2 Douady, Adrien 2 Fibich, Gadi 2 Filippas, Stathis 2 Glangetas, Léo 2 Golse, François 2 Jia, Hao 2 Rivière, Tristan 2 Tsai, Tai-Peng 2 Tsutsumi, Yoshio 2 Vega, Luis 1 Antonini, Christophe 1 Fermanian-Kammerer, Clotilde 1 Mizumachi, Tetsu 1 Nakanishi, Kenji 1 Roudenko, Svetlana 1 Serrin, James all top 5 Serials 15 Communications in Mathematical Physics 9 Comptes Rendus de l’Académie des Sciences. Série I 8 IMRN. International Mathematics Research Notices 7 Communications on Pure and Applied Mathematics 7 Geometric and Functional Analysis. GAFA 7 Séminaire Équations aux Dérivées Partielles 6 Archive for Rational Mechanics and Analysis 6 Duke Mathematical Journal 5 American Journal of Mathematics 5 Inventiones Mathematicae 5 Journal of Functional Analysis 4 Mathematische Annalen 4 Journal of the American Mathematical Society 4 Discrete and Continuous Dynamical Systems 4 Journal of the European Mathematical Society (JEMS) 4 Networks and Heterogeneous Media 3 Journal of Differential Equations 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Annals of Mathematics. Second Series 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 Nonlinearity 2 Acta Mathematica 2 Indiana University Mathematics Journal 2 Transactions of the American Mathematical Society 2 Physica D 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Cambridge Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Russian Mathematical Surveys 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Revista Matemática Iberoamericana 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Methods and Applications of Analysis 1 Bulletin des Sciences Mathématiques 1 Documenta Mathematica 1 Revista Matemática Complutense 1 Communications on Pure and Applied Analysis 1 Journal of Hyperbolic Differential Equations 1 IMRP. International Mathematics Research Papers 1 Séminaire Laurent Schwartz. EDP et Applications all top 5 Fields 154 Partial differential equations (35-XX) 22 Dynamical systems and ergodic theory (37-XX) 5 Fluid mechanics (76-XX) 3 Quantum theory (81-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Ordinary differential equations (34-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 131 Publications have been cited 4,337 times in 1,661 Documents Cited by ▼ Year ▼ Uniform estimates and blow-up behavior for solutions of \(-\Delta{} u =V(x) e^ u\) in two dimensions. Zbl 0746.35006Brézis, Haïm; Merle, Frank 324 1991 Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrödinger equation in the radial case. Zbl 1115.35125Kenig, Carlos E.; Merle, Frank 276 2006 Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202Kenig, Carlos E.; Merle, Frank 183 2008 The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263Merle, Frank; Raphaël, Pierre 113 2005 On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110Merle, Frank; Raphaël, Pierre 98 2004 Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Zbl 0808.35141Merle, F. 96 1993 Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity. Zbl 0707.35021Merle, Frank 87 1990 Compactness at blow-up time for \(L^2\) solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126Merle, F.; Vega, L. 81 1998 L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. Zbl 0722.35047Merle, Frank; Tsutsumi, Yoshio 74 1990 On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098Matano, Hiroshi; Merle, Frank 72 2004 Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098Martel, Yvan; Merle, Frank; Tsai, Tai-Peng 72 2002 On a sharp lower bound on the blow-up rate for the \(L^2\) critical nonlinear Schrödinger equation. Zbl 1075.35077Merle, Frank; Raphaël, Pierre 71 2006 Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137Merle, Frank; Raphaël, Pierre 71 2005 Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135Merle, Frank; Raphaël, Pierre 69 2003 Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 65 2013 Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073Martel, Yvan; Merle, Frank 64 2001 Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation. Zbl 1230.35067Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 61 2011 Stability of the blow-up profile for equations of the type \(u_ t=\Delta u+| u| ^{p-1}u\). Zbl 0872.35049Merle, Frank; Zaag, Hatem 59 1997 Blow up in finite time and dynamics of blow up solutions for the \(L^2\)-critical generalized KdV equation. Zbl 0996.35064Martel, Yvan; Merle, Frank 58 2002 Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128Merle, Frank 58 2001 A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058Martel, Yvan; Merle, Frank 57 2000 Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044Merle, Frank; Zaag, Hatem 54 1998 Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071Martel, Y.; Merle, F. 51 2001 Scattering for \(\dot {H}^{1/2}\) bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180Kenig, Carlos E.; Merle, Frank 50 2010 Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084Matano, Hiroshi; Merle, Frank 50 2009 Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171Martel, Yvan; Merle, Frank 50 2005 Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150Duyckaerts, Thomas; Merle, Frank 49 2009 Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081Martel, Yvan; Merle, Frank 49 2002 Solution of a nonlinear heat equation with arbitrarily given blow-up points. Zbl 0785.35012Merle, Frank 49 1992 Existence of stationary states for nonlinear Dirac equations. Zbl 0696.35154Merle, F. 49 1988 Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043Duyckaerts, Thomas; Merle, Frank 47 2008 Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\). Zbl 0809.35019Brézis, Haïm; Merle, Frank; Rivière, Tristan 47 1994 Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 46 2012 Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. Zbl 1282.35088Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 44 2012 Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093Martel, Yvan; Merle, Frank 44 2006 Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations. Zbl 1099.35134Martel, Yvan; Merle, Frank; Tsai, Tai-Peng 43 2006 A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086Merle, Frank; Zaag, Hatem 43 2000 Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136Kenig, Carlos E.; Merle, Frank 41 2011 Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043Merle, Frank; Zaag, Hatem 40 2003 On uniqueness and continuation properties after blow-up time of self- similar solutions of nonlinear Schrödinger equation with critical exponent and critical mass. Zbl 0767.35084Merle, Frank 39 1992 Existence of excited states for a nonlinear Dirac field. Zbl 0696.35158Balabane, Mikhael; Cazenave, Thierry; Douady, Adrien; Merle, Frank 39 1988 Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 38 2013 Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055Merle, Frank; Zaag, Hatem 38 2005 Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070Merle, Frank; Zaag, Hatem 37 2007 Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Zbl 0808.35137Glangetas, L.; Merle, F. 37 1994 Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234Côte, Raphaël; Martel, Yvan; Merle, Frank 36 2011 Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1252.35204Merle, Frank; Zaag, Hatem 34 2012 Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II. Zbl 0808.35138Glangetas, L.; Merle, F. 34 1994 Nonexistence of minimal blow-up solutions of equations \(iu_ t = -\Delta u - k(x)| u|^{4/N} u\) in \(\mathbb{R}^ N\). Zbl 0846.35129Merle, Franck 33 1996 Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068Martel, Yvan; Merle, Frank 32 2008 Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation. Zbl 1159.35046Merle, Frank; Zaag, Hatem 31 2008 Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137Martel, Yvan; Merle, Frank; Raphaël, Pierre 30 2014 Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307Martel, Yvan; Merle, Frank; Raphaël, Pierre 29 2015 Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 29 2014 Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045Martel, Yvan; Merle, Frank 28 2011 Stability of the blow-up profile of nonlinear heat equations from the dynamical system point of view. Zbl 0971.35038Fermanian Kammerer, C.; Merle, F.; Zaag, H. 27 2000 Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024Merle, F.; Zaag, H. 26 1998 Proof of a spectral property related to the singularity formation for the \(L^{2}\) critical nonlinear Schrödinger equation. Zbl 1100.35097Fibich, Gadi; Merle, Frank; Raphaël, Pierre 25 2006 \(L^2\) stability of solitons for KdV equation. Zbl 1022.35061Merle, F.; Vega, L. 25 2003 Positive solutions of elliptic equations involving supercritical growth. Zbl 0742.35025Merle, F.; Peletier, L. A. 25 1991 Soliton resolution along a sequence of times for the focusing energy critical wave equation. Zbl 1391.35276Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank 24 2017 Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320Martel, Yvan; Merle, Frank; Raphaël, Pierre 24 2015 Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088Matano, Hiroshi; Merle, Frank 24 2011 On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Zbl 1315.35134Merle, Frank; Zaag, Hatem 23 2015 Blow-up results of virial type for Zakharov equations. Zbl 0858.35117Merle, Frank 23 1996 On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478Merle, Frank; Zaag, Hatem 22 2005 Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291Martel, Yvan; Merle, Frank 21 2009 Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320Merle, Frank; Zaag, Hatem 20 2012 Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090Antonini, Christophe; Merle, Frank 20 2001 Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. I: The radial case. Zbl 0719.35004Merle, F.; Peletier, L. A. 20 1990 Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 19 2010 Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182Merle, Frank; Raphaël, Pierre 19 2008 Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102Martel, Yvan; Merle, Frank 19 2002 Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178Collot, Charles; Merle, Frank; Raphaël, Pierre 18 2017 Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121Martel, Yvan; Merle, Frank 18 2011 Type II blow up for the energy supercritical NLS. Zbl 1347.35215Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 17 2015 Limit of the solution of a nonlinear Schrödinger equation at blow-up time. Zbl 0681.35078Merle, F. 17 1989 Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 16 2016 Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. Zbl 1213.35139Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 16 2011 Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre 15 2016 The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 15 2013 Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119Kenig, Carlos E.; Merle, Frank 15 2011 Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system. Zbl 1170.35064Côte, Raphaël; Kenig, Carlos E.; Merle, Frank 15 2008 Self-focusing on bounded domains. Zbl 0980.35154Fibich, Gadi; Merle, Frank 15 2001 Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. II: The nonradial case. Zbl 0771.35008Merle, F.; Peletier, L. A. 15 1992 Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126Merle, Frank; Zaag, Hatem 14 2011 Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Zbl 1339.35062Merle, Frank; Zaag, Hatem 13 2016 Modulation theory for the blowup of vector-valued nonlinear heat equations. Zbl 0814.35043Filippas, Stathis; Merle, Frank 13 1995 Lower bounds for the blowup rate of solutions of the Zakharov equation in dimension two. Zbl 0856.35014Merle, Frank 12 1996 Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166Martel, Yvan; Merle, Frank 11 2016 Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062Martel, Yvan; Merle, Frank 11 2008 Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. Zbl 1320.35066Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 10 2015 On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 10 2014 Reconnection of vortex with the boundary and finite time quenching. Zbl 0910.35020Merle, Frank; Zaag, Hatem 10 1997 Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 9 2016 Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267Martel, Yvan; Merle, Frank; Mizumachi, Tetsu 9 2010 Limit behavior of saturated approximations of nonlinear Schrödinger equation. Zbl 0756.35094Merle, F. 9 1992 On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075Merle, Frank; Raphael, Pierre 8 2005 O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039Merle, Frank; Zaag, Hatem 8 2002 Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg-de Vries equation. Zbl 1219.35248Martel, Yvan; Merle, Frank 6 2011 Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253Collot, Charles; Merle, Frank; Raphaël, Pierre 2 2020 Exterior energy bounds for the critical wave equation close to the ground state. Zbl 1450.35157Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 1 2020 On strongly anisotropic type I blowup. Zbl 1432.35124Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 1 2020 Scattering profile for global solutions of the energy-critical wave equation. Zbl 1437.35497Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 2 2019 Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111Martel, Yvan; Merle, Frank 2 2018 Blowup solutions to the semilinear wave equation with a stylized pyramid as a blowup surface. Zbl 1402.35181Merle, Frank; Zaag, Hatem 1 2018 Soliton resolution along a sequence of times for the focusing energy critical wave equation. Zbl 1391.35276Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank 24 2017 Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178Collot, Charles; Merle, Frank; Raphaël, Pierre 18 2017 Stability of ODE blow-up for the energy critical semilinear heat equation. Zbl 1364.35156Collot, Charles; Merle, Frank; Raphaël, Pierre 5 2017 Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 16 2016 Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre 15 2016 Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Zbl 1339.35062Merle, Frank; Zaag, Hatem 13 2016 Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166Martel, Yvan; Merle, Frank 11 2016 Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 9 2016 Global existence for solutions of the focusing wave equation with the compactness property. Zbl 1362.35190Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 2 2016 Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307Martel, Yvan; Merle, Frank; Raphaël, Pierre 29 2015 Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320Martel, Yvan; Merle, Frank; Raphaël, Pierre 24 2015 On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Zbl 1315.35134Merle, Frank; Zaag, Hatem 23 2015 Type II blow up for the energy supercritical NLS. Zbl 1347.35215Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 17 2015 Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. Zbl 1320.35066Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 10 2015 On the nonexistence of pure multi-solitons for the quartic gKdV equation. Zbl 1315.35191Martel, Yvan; Merle, Frank 3 2015 Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137Martel, Yvan; Merle, Frank; Raphaël, Pierre 30 2014 Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 29 2014 On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 10 2014 Near soliton dynamics and singularity formation for \( L^2\) critical problems. Zbl 1304.35650Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J. 3 2014 Asymptotics for critical nonlinear dispersive equations. Zbl 1373.35049Merle, Frank 1 2014 Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 65 2013 Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 38 2013 The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 15 2013 Blow up and near soliton dynamics for the \(L^2\) critical gKdV equation. Zbl 1319.35224Martel, Yvan; Merle, Frank; Raphaël, Pierre 4 2013 Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 46 2012 Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. Zbl 1282.35088Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 44 2012 Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1252.35204Merle, Frank; Zaag, Hatem 34 2012 Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320Merle, Frank; Zaag, Hatem 20 2012 Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1280.35019Merle, Frank 2 2012 Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation. Zbl 1230.35067Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 61 2011 Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136Kenig, Carlos E.; Merle, Frank 41 2011 Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234Côte, Raphaël; Martel, Yvan; Merle, Frank 36 2011 Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045Martel, Yvan; Merle, Frank 28 2011 Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088Matano, Hiroshi; Merle, Frank 24 2011 Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121Martel, Yvan; Merle, Frank 18 2011 Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. Zbl 1213.35139Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 16 2011 Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119Kenig, Carlos E.; Merle, Frank 15 2011 Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126Merle, Frank; Zaag, Hatem 14 2011 Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg-de Vries equation. Zbl 1219.35248Martel, Yvan; Merle, Frank 6 2011 Maximizers for the Strichartz norm for small solutions of mass-critical NLS. Zbl 1247.35142Duyckaerts, Thomas; Merle, Frank; Roudenko, Svetlana 5 2011 Scattering for \(\dot {H}^{1/2}\) bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180Kenig, Carlos E.; Merle, Frank 50 2010 Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 19 2010 Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267Martel, Yvan; Merle, Frank; Mizumachi, Tetsu 9 2010 Inelastic interaction of nearly equal solitons for the BBM equation. Zbl 1188.35165Martel, Yvan; Merle, Frank 4 2010 Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084Matano, Hiroshi; Merle, Frank 50 2009 Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150Duyckaerts, Thomas; Merle, Frank 49 2009 Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291Martel, Yvan; Merle, Frank 21 2009 Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202Kenig, Carlos E.; Merle, Frank 183 2008 Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043Duyckaerts, Thomas; Merle, Frank 47 2008 Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068Martel, Yvan; Merle, Frank 32 2008 Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation. Zbl 1159.35046Merle, Frank; Zaag, Hatem 31 2008 Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182Merle, Frank; Raphaël, Pierre 19 2008 Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system. Zbl 1170.35064Côte, Raphaël; Kenig, Carlos E.; Merle, Frank 15 2008 Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062Martel, Yvan; Merle, Frank 11 2008 Note on coupled linear systems related to two soliton collision for the quartic gKdV equation. Zbl 1188.35164Martel, Yvan; Merle, Frank 4 2008 Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070Merle, Frank; Zaag, Hatem 37 2007 On the energy critical focusing non-linear wave equation. Zbl 1173.35601Merle, Frank 1 2007 Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrödinger equation in the radial case. Zbl 1115.35125Kenig, Carlos E.; Merle, Frank 276 2006 On a sharp lower bound on the blow-up rate for the \(L^2\) critical nonlinear Schrödinger equation. Zbl 1075.35077Merle, Frank; Raphaël, Pierre 71 2006 Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093Martel, Yvan; Merle, Frank 44 2006 Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations. Zbl 1099.35134Martel, Yvan; Merle, Frank; Tsai, Tai-Peng 43 2006 Proof of a spectral property related to the singularity formation for the \(L^{2}\) critical nonlinear Schrödinger equation. Zbl 1100.35097Fibich, Gadi; Merle, Frank; Raphaël, Pierre 25 2006 Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders. Zbl 1105.35051Kenig, Carlos E.; Merle, Frank 3 2006 The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263Merle, Frank; Raphaël, Pierre 113 2005 Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137Merle, Frank; Raphaël, Pierre 71 2005 Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171Martel, Yvan; Merle, Frank 50 2005 Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055Merle, Frank; Zaag, Hatem 38 2005 On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478Merle, Frank; Zaag, Hatem 22 2005 On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075Merle, Frank; Raphael, Pierre 8 2005 On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110Merle, Frank; Raphaël, Pierre 98 2004 On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098Matano, Hiroshi; Merle, Frank 72 2004 Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations. Zbl 1071.35114Martel, Yvan; Merle, Frank 3 2004 Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135Merle, Frank; Raphaël, Pierre 69 2003 Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043Merle, Frank; Zaag, Hatem 40 2003 \(L^2\) stability of solitons for KdV equation. Zbl 1022.35061Merle, F.; Vega, L. 25 2003 Qualitative results on the generalized critical KdV equation. Zbl 1044.35074Martel, Yvan; Merle, Frank 1 2003 Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098Martel, Yvan; Merle, Frank; Tsai, Tai-Peng 72 2002 Blow up in finite time and dynamics of blow up solutions for the \(L^2\)-critical generalized KdV equation. Zbl 0996.35064Martel, Yvan; Merle, Frank 58 2002 Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081Martel, Yvan; Merle, Frank 49 2002 Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102Martel, Yvan; Merle, Frank 19 2002 O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039Merle, Frank; Zaag, Hatem 8 2002 Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073Martel, Yvan; Merle, Frank 64 2001 Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128Merle, Frank 58 2001 Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071Martel, Y.; Merle, F. 51 2001 Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090Antonini, Christophe; Merle, Frank 20 2001 Self-focusing on bounded domains. Zbl 0980.35154Fibich, Gadi; Merle, Frank 15 2001 Uniform blow-up estimates for nonlinear heat equations and applications. Zbl 1019.35044Merle, Frank; Zaag, Hatem 2 2001 A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058Martel, Yvan; Merle, Frank 57 2000 A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086Merle, Frank; Zaag, Hatem 43 2000 Stability of the blow-up profile of nonlinear heat equations from the dynamical system point of view. Zbl 0971.35038Fermanian Kammerer, C.; Merle, F.; Zaag, H. 27 2000 Compactness at blow-up time for \(L^2\) solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126Merle, F.; Vega, L. 81 1998 Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044Merle, Frank; Zaag, Hatem 54 1998 Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024Merle, F.; Zaag, H. 26 1998 Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations. Zbl 0896.35123Merle, Frank 5 1998 ...and 31 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,330 Authors 67 Merle, Frank 39 Martel, Yvan 39 Wei, Juncheng 37 Raphael, Pierre 36 Zaag, Hatem 32 Kenig, Carlos Eduardo 31 Bartolucci, Daniele 28 Lin, Chang-Shou 24 Muñoz, Claudio 22 Krieger, Joachim 22 Musso, Monica 18 Schlag, Wilhelm 18 Zhang, Jian 17 Del Pino, Manuel A. 17 Ding, Yanheng 17 Donninger, Roland 17 Miao, Changxing 17 Souplet, Philippe 16 Mizoguchi, Noriko 16 Nakanishi, Kenji 16 Tarantello, Gabriella 16 Zhao, Lifeng 16 Zhu, Shihui 15 Duyckaerts, Thomas 15 Guo, Boling 15 Saanouni, Tarek 14 Côte, Raphaël 14 Martinazzi, Luca 14 Zheng, Jiqiang 14 Zhou, Chunqin 13 Holmer, Justin 13 Malchiodi, Andrea 13 Roudenko, Svetlana 13 Suzuki, Takashi 13 Visan, Monica 13 Yang, Wen 12 Tataru, Daniel 12 Xu, Guixiang 11 Farah, Luiz Gustavo 11 Jevnikar, Aleks 11 Lawrie, Andrew G. W. 11 Wang, Guofang 11 Zhang, Xiaoyi 10 Bahouri, Hajer 10 Cazenave, Thierry 10 Jost, Jürgen 10 Killip, Rowan 10 Lee, Youngae 10 Nguyen, Van Tien 9 Fibich, Gadi 9 Ghoul, Tej-Eddine 9 Ibrahim, Slim 9 Miyamoto, Yasuhito 8 Carles, Rémi 8 Colliander, James E. 8 Cuccagna, Scipio 8 Dodson, Benjamin G. 8 Fang, Daoyuan 8 Galaktionov, Victor Aleksandrovich 8 Gan, Zaihui 8 Grossi, Massimo 8 Klein, Christian 8 Lenzmann, Enno 8 Li, Dong 8 Li, Xiaoguang 8 Masmoudi, Nader 8 Pausader, Benoît 8 Pistoia, Angela 8 Struwe, Michael 8 Tao, Terence 8 Tzvetkov, Nikolay 8 Zhang, Lei 7 Banica, Valeria 7 Cheng, Xing 7 Choe, Kwangseok 7 Deng, Shengbing 7 Gao, Yanfang 7 Guo, Zihua 7 Hamza, Mohamed Ali 7 Ishige, Kazuhiro 7 Lei, Yutian 7 Liu, Yue 7 Mizumachi, Tetsu 7 Murphy, Jason 7 Perelman, Galina 7 Ponce, Gustavo 7 Saut, Jean-Claude 7 Visciglia, Nicola 6 Battaglia, Luca 6 Chanillo, Sagun 6 Cho, Yonggeun 6 Collot, Charles 6 D’Aprile, Teresa 6 de Marchis, Francesca 6 Dinh, Van Duong 6 Dolbeault, Jean 6 Fujishima, Yohei 6 Guo, Jong-Shenq 6 Guo, Qing 6 Jendrej, Jacek ...and 1,230 more Authors all top 5 Cited in 222 Serials 146 Journal of Differential Equations 81 Journal of Functional Analysis 70 Communications in Mathematical Physics 70 Journal of Mathematical Analysis and Applications 69 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 67 Calculus of Variations and Partial Differential Equations 62 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 53 Communications in Partial Differential Equations 49 Discrete and Continuous Dynamical Systems 48 Transactions of the American Mathematical Society 42 Journal of Mathematical Physics 32 Archive for Rational Mechanics and Analysis 31 Communications on Pure and Applied Analysis 30 Mathematische Annalen 24 Journal de Mathématiques Pures et Appliquées. Neuvième Série 24 Communications in Contemporary Mathematics 23 Physica D 22 Duke Mathematical Journal 21 Proceedings of the American Mathematical Society 19 Advances in Mathematics 19 Acta Mathematica Sinica. English Series 17 Communications on Pure and Applied Mathematics 17 Comptes Rendus. Mathématique. 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Series B 5 Milan Journal of Mathematics 4 Computers & Mathematics with Applications 4 Reviews in Mathematical Physics 4 Indiana University Mathematics Journal 4 Journal of Computational and Applied Mathematics 4 The Journal of Geometric Analysis 4 Communications in Mathematics and Statistics 4 Journal of Elliptic and Parabolic Equations 3 Mathematics of Computation 3 Acta Mathematica 3 Annales de l’Institut Fourier 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Illinois Journal of Mathematics 3 Proceedings of the London Mathematical Society. Third Series 3 SIAM Journal on Numerical Analysis 3 Asymptotic Analysis 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Annals of Mathematics. Second Series 3 Communications in Nonlinear Science and Numerical Simulation 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 Mediterranean Journal of Mathematics 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 3 Journal of Fixed Point Theory and Applications 3 Frontiers of Mathematics in China 3 Kyoto Journal of Mathematics 2 Journal of Statistical Physics 2 Letters in Mathematical Physics 2 Rocky Mountain Journal of Mathematics 2 Wave Motion 2 Bulletin de la Société Mathématique de France 2 Czechoslovak Mathematical Journal 2 Publications Mathématiques 2 Journal für die Reine und Angewandte Mathematik 2 Monatshefte für Mathematik 2 Numerische Mathematik 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Rendiconti del Seminario Matematico della Università di Padova 2 Studies in Applied Mathematics ...and 122 more Serials all top 5 Cited in 46 Fields 1,576 Partial differential equations (35-XX) 111 Dynamical systems and ergodic theory (37-XX) 111 Global analysis, analysis on manifolds (58-XX) 105 Quantum theory (81-XX) 99 Fluid mechanics (76-XX) 76 Differential geometry (53-XX) 56 Numerical analysis (65-XX) 49 Operator theory (47-XX) 47 Statistical mechanics, structure of matter (82-XX) 39 Calculus of variations and optimal control; optimization (49-XX) 38 Functional analysis (46-XX) 31 Optics, electromagnetic theory (78-XX) 30 Ordinary differential equations (34-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 20 Biology and other natural sciences (92-XX) 17 Mechanics of deformable solids (74-XX) 14 Real functions (26-XX) 11 Functions of a complex variable (30-XX) 11 Relativity and gravitational theory (83-XX) 10 Mechanics of particles and systems (70-XX) 9 Probability theory and stochastic processes (60-XX) 8 Systems theory; control (93-XX) 6 Potential theory (31-XX) 6 Astronomy and astrophysics (85-XX) 5 Special functions (33-XX) 5 Integral equations (45-XX) 4 Difference and functional equations (39-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Statistics (62-XX) 2 History and biography (01-XX) 2 Nonassociative rings and algebras (17-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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