Edit Profile (opens in new tab) Merle, Frank Compute Distance To: Compute Author ID: merle.frank Published as: Merle, Frank; Merle, F.; Merle, Franck Homepage: https://www.ihes.fr/en/professeur/frank-merle-2/ External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · dblp · IdRef · theses.fr Documents Indexed: 156 Publications since 1987 4 Contributions as Editor Co-Authors: 32 Co-Authors with 134 Joint Publications 1,114 Co-Co-Authors all top 5 Co-Authors 26 single-authored 35 Martel, Yvan 26 Raphael, Pierre 24 Kenig, Carlos Eduardo 22 Zaag, Hatem 20 Duyckaerts, Thomas 7 Szeftel, Jérémie 5 Peletier, Lambertus Adrianus 4 Berestycki, Henri 4 Hilhorst, Danielle 4 Mimura, Masayasu 4 Pakdaman, Khashayar 4 Rodnianski, Igor 3 Brézis, Haïm 3 Collot, Charles 3 Matano, Hiroshi 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 Rivière, Tristan 2 Tsai, Tai-Peng 2 Tsutsumi, Yoshio 2 Vega, Luis 1 Antonini, Christophe 1 Fermanian-Kammerer, Clotilde 1 Mizumachi, Tetsu 1 Roudenko, Svetlana 1 Serrin, James all top 5 Serials 16 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 6 Inventiones Mathematicae 5 American Journal of Mathematics 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 2 Séminaire Laurent Schwartz. EDP et Applications 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 The Journal of Geometric Analysis 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 all top 5 Fields 158 Partial differential equations (35-XX) 22 Dynamical systems and ergodic theory (37-XX) 6 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 134 Publications have been cited 4,839 times in 1,857 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 354 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 323 2006 Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202Kenig, Carlos E.; Merle, Frank 208 2008 The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263Merle, Frank; Raphaël, Pierre 130 2005 Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Zbl 0808.35141Merle, F. 107 1993 On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110Merle, Frank; Raphaël, Pierre 104 2004 Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity. Zbl 0707.35021Merle, Frank 95 1990 Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098Martel, Yvan; Merle, Frank; Tsai, Tai-Peng 87 2002 Compactness at blow-up time for \(L^2\) solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126Merle, F.; Vega, L. 86 1998 On a sharp lower bound on the blow-up rate for the \(L^2\) critical nonlinear Schrödinger equation. Zbl 1075.35077Merle, Frank; Raphaël, Pierre 81 2006 On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098Matano, Hiroshi; Merle, Frank 80 2004 Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 77 2013 Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135Merle, Frank; Raphaël, Pierre 76 2003 L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. Zbl 0722.35047Merle, Frank; Tsutsumi, Yoshio 75 1990 Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073Martel, Yvan; Merle, Frank 75 2001 Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137Merle, Frank; Raphaël, Pierre 74 2005 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 72 1997 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 69 2011 A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058Martel, Yvan; Merle, Frank 67 2000 Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128Merle, Frank 66 2001 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 65 2002 Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071Martel, Y.; Merle, F. 59 2001 Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171Martel, Yvan; Merle, Frank 58 2005 Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084Matano, Hiroshi; Merle, Frank 55 2009 Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150Duyckaerts, Thomas; Merle, Frank 55 2009 Existence of stationary states for nonlinear Dirac equations. Zbl 0696.35154Merle, F. 54 1988 Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093Martel, Yvan; Merle, Frank 52 2006 Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081Martel, Yvan; Merle, Frank 52 2002 Solution of a nonlinear heat equation with arbitrarily given blow-up points. Zbl 0785.35012Merle, Frank 52 1992 Scattering for \(\dot {H}^{1/2}\) bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180Kenig, Carlos E.; Merle, Frank 51 2010 Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043Duyckaerts, Thomas; Merle, Frank 51 2008 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 50 2006 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 50 2012 Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\). Zbl 0809.35019Brézis, Haïm; Merle, Frank; Rivière, Tristan 50 1994 Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 47 2012 Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234Côte, Raphaël; Martel, Yvan; Merle, Frank 47 2011 A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086Merle, Frank; Zaag, Hatem 46 2000 Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 46 2013 Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043Merle, Frank; Zaag, Hatem 43 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 42 1992 Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136Kenig, Carlos E.; Merle, Frank 42 2011 Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070Merle, Frank; Zaag, Hatem 41 2007 Existence of excited states for a nonlinear Dirac field. Zbl 0696.35158Balabane, Mikhael; Cazenave, Thierry; Douady, Adrien; Merle, Frank 41 1988 Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055Merle, Frank; Zaag, Hatem 41 2005 Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Zbl 0808.35137Glangetas, L.; Merle, F. 40 1994 Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068Martel, Yvan; Merle, Frank 39 2008 Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1252.35204Merle, Frank; Zaag, Hatem 38 2012 Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137Martel, Yvan; Merle, Frank; Raphaël, Pierre 36 2014 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 36 1996 Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044Merle, Frank; Zaag, Hatem 35 1998 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 35 2008 Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II. Zbl 0808.35138Glangetas, L.; Merle, F. 35 1994 Soliton resolution along a sequence of times for the focusing energy critical wave equation. Zbl 1391.35276Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank 34 2017 Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 32 2014 Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045Martel, Yvan; Merle, Frank 31 2011 Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307Martel, Yvan; Merle, Frank; Raphaël, Pierre 30 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 30 2015 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. 29 2000 \(L^2\) stability of solitons for KdV equation. Zbl 1022.35061Merle, F.; Vega, L. 29 2003 Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088Matano, Hiroshi; Merle, Frank 28 2011 Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024Merle, F.; Zaag, H. 28 1998 Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320Martel, Yvan; Merle, Frank; Raphaël, Pierre 27 2015 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 27 2006 Positive solutions of elliptic equations involving supercritical growth. Zbl 0742.35025Merle, F.; Peletier, L. A. 26 1991 Blow-up results of virial type for Zakharov equations. Zbl 0858.35117Merle, Frank 25 1996 Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320Merle, Frank; Zaag, Hatem 25 2012 Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178Collot, Charles; Merle, Frank; Raphaël, Pierre 25 2017 Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182Merle, Frank; Raphaël, Pierre 23 2008 Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 22 2016 Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090Antonini, Christophe; Merle, Frank 22 2001 Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121Martel, Yvan; Merle, Frank 21 2011 Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291Martel, Yvan; Merle, Frank 21 2009 Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102Martel, Yvan; Merle, Frank 21 2002 On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478Merle, Frank; Zaag, Hatem 21 2005 Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 20 2010 Type II blow up for the energy supercritical NLS. Zbl 1347.35215Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 19 2015 Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. I: The radial case. Zbl 0719.35004Merle, F.; Peletier, L. A. 19 1990 Limit of the solution of a nonlinear Schrödinger equation at blow-up time. Zbl 0681.35078Merle, F. 18 1989 Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. (Dynamique explosive de solutions régulières équivariantes de l’application de Schrödinger map.) Zbl 1213.35139Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 17 2011 Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre 17 2016 The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 17 2013 Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Zbl 1339.35062Merle, Frank; Zaag, Hatem 16 2016 Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. II: The nonradial case. Zbl 0771.35008Merle, F.; Peletier, L. A. 16 1992 Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126Merle, Frank; Zaag, Hatem 16 2011 Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119Kenig, Carlos E.; Merle, Frank 16 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 16 2008 Self-focusing on bounded domains. Zbl 0980.35154Fibich, Gadi; Merle, Frank 15 2001 Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166Martel, Yvan; Merle, Frank 14 2016 On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 13 2014 Lower bounds for the blowup rate of solutions of the Zakharov equation in dimension two. Zbl 0856.35014Merle, Frank 13 1996 Reconnection of vortex with the boundary and finite time quenching. Zbl 0910.35020Merle, Frank; Zaag, Hatem 12 1997 Modulation theory for the blowup of vector-valued nonlinear heat equations. Zbl 0814.35043Filippas, Stathis; Merle, Frank 12 1995 Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062Martel, Yvan; Merle, Frank 12 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 11 2015 Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 11 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 O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039Merle, Frank; Zaag, Hatem 9 2002 On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075Merle, Frank; Raphael, Pierre 8 2005 Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253Collot, Charles; Merle, Frank; Raphaël, Pierre 8 2020 On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Zbl 07470584Merle, Frank; Raphaël, Pierre; Rodnianski, Igor; Szeftel, Jeremie 1 2022 Decay estimates for nonradiative solutions of the energy-critical focusing wave equation. Zbl 1472.35050Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 1 2021 Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253Collot, Charles; Merle, Frank; Raphaël, Pierre 8 2020 On strongly anisotropic type I blowup. Zbl 1432.35124Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 3 2020 Exterior energy bounds for the critical wave equation close to the ground state. Zbl 1450.35157Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 3 2020 Scattering profile for global solutions of the energy-critical wave equation. Zbl 1437.35497Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 5 2019 Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111Martel, Yvan; Merle, Frank 3 2018 Universality of blow up profile for small blow up solutions to the energy critical wave map equation. Zbl 1421.35038Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; 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 34 2017 Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178Collot, Charles; Merle, Frank; Raphaël, Pierre 25 2017 Stability of ODE blow-up for the energy critical semilinear heat equation. (Stabilité de l’explosion type EDO pour l’équation de la chaleur énergie critique.) Zbl 1364.35156Collot, Charles; Merle, Frank; Raphaël, Pierre 6 2017 Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 22 2016 Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre 17 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 16 2016 Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166Martel, Yvan; Merle, Frank 14 2016 Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 11 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 30 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 30 2015 Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320Martel, Yvan; Merle, Frank; Raphaël, Pierre 27 2015 Type II blow up for the energy supercritical NLS. Zbl 1347.35215Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 19 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 11 2015 On the nonexistence of pure multi-solitons for the quartic gKdV equation. Zbl 1315.35191Martel, Yvan; Merle, Frank 4 2015 Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137Martel, Yvan; Merle, Frank; Raphaël, Pierre 36 2014 Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 32 2014 On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 13 2014 Near soliton dynamics and singularity formation for \( L^2\) critical problems. Zbl 1304.35650Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J. 4 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 77 2013 Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 46 2013 The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 17 2013 Blow up and near soliton dynamics for the \(L^2\) critical gKdV equation. Zbl 1319.35224Martel, Yvan; Merle, Frank; Raphaël, Pierre 4 2013 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 50 2012 Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 47 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 38 2012 Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320Merle, Frank; Zaag, Hatem 25 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 69 2011 Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234Côte, Raphaël; Martel, Yvan; Merle, Frank 47 2011 Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136Kenig, Carlos E.; Merle, Frank 42 2011 Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045Martel, Yvan; Merle, Frank 31 2011 Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088Matano, Hiroshi; Merle, Frank 28 2011 Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121Martel, Yvan; Merle, Frank 21 2011 Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map. (Dynamique explosive de solutions régulières équivariantes de l’application de Schrödinger map.) Zbl 1213.35139Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 17 2011 Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126Merle, Frank; Zaag, Hatem 16 2011 Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119Kenig, Carlos E.; Merle, Frank 16 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 51 2010 Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 20 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 55 2009 Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150Duyckaerts, Thomas; Merle, Frank 55 2009 Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291Martel, Yvan; Merle, Frank 21 2009 Scattering norm estimate near the threshold for energy-critical focusing semilinear wave equation. Zbl 1179.35189Duyckaerts, Thomas; Merle, Frank 1 2009 Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202Kenig, Carlos E.; Merle, Frank 208 2008 Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043Duyckaerts, Thomas; Merle, Frank 51 2008 Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068Martel, Yvan; Merle, Frank 39 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 35 2008 Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182Merle, Frank; Raphaël, Pierre 23 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 16 2008 Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062Martel, Yvan; Merle, Frank 12 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 41 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 323 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 81 2006 Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093Martel, Yvan; Merle, Frank 52 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 50 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 27 2006 Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders. Zbl 1105.35051Kenig, Carlos E.; Merle, Frank 4 2006 The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263Merle, Frank; Raphaël, Pierre 130 2005 Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137Merle, Frank; Raphaël, Pierre 74 2005 Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171Martel, Yvan; Merle, Frank 58 2005 Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055Merle, Frank; Zaag, Hatem 41 2005 On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478Merle, Frank; Zaag, Hatem 21 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 104 2004 On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098Matano, Hiroshi; Merle, Frank 80 2004 Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations. Zbl 1071.35114Martel, Yvan; Merle, Frank 2 2004 Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135Merle, Frank; Raphaël, Pierre 76 2003 Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043Merle, Frank; Zaag, Hatem 43 2003 \(L^2\) stability of solitons for KdV equation. Zbl 1022.35061Merle, F.; Vega, L. 29 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 87 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 65 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 52 2002 Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102Martel, Yvan; Merle, Frank 21 2002 O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039Merle, Frank; Zaag, Hatem 9 2002 Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073Martel, Yvan; Merle, Frank 75 2001 Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128Merle, Frank 66 2001 Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071Martel, Y.; Merle, F. 59 2001 Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090Antonini, Christophe; Merle, Frank 22 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 1 2001 A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058Martel, Yvan; Merle, Frank 67 2000 A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086Merle, Frank; Zaag, Hatem 46 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. 29 2000 Compactness at blow-up time for \(L^2\) solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126Merle, F.; Vega, L. 86 1998 ...and 34 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,385 Authors 71 Merle, Frank 44 Martel, Yvan 42 Zaag, Hatem 41 Wei, Juncheng 38 Raphael, Pierre 34 Kenig, Carlos Eduardo 31 Bartolucci, Daniele 29 Lin, Chang-Shou 28 Muñoz, Claudio 25 Musso, Monica 22 Krieger, Joachim 21 Duyckaerts, Thomas 20 Saanouni, Tarek 18 Côte, Raphaël 18 Del Pino, Manuel A. 18 Ding, Yanheng 18 Schlag, Wilhelm 18 Zhao, Lifeng 17 Donninger, Roland 17 Miao, Changxing 17 Roudenko, Svetlana 16 Mizoguchi, Noriko 16 Souplet, Philippe 16 Tarantello, Gabriella 16 Zhang, Jian 16 Zhu, Shihui 15 Dinh, Van Duong 15 Guo, Boling 15 Holmer, Justin 15 Martinazzi, Luca 15 Nakanishi, Kenji 15 Visan, Monica 15 Zheng, Jiqiang 15 Zhou, Chunqin 14 Lee, Youngae 14 Yang, Wen 13 Malchiodi, Andrea 13 Suzuki, Takashi 13 Tataru, Daniel 12 Dodson, Benjamin G. 12 Farah, Luiz Gustavo 12 Killip, Rowan 12 Wang, Guofang 12 Xu, Guixiang 12 Zhang, Xiaoyi 11 Bahouri, Hajer 11 Ibrahim, Slim 11 Jevnikar, Aleks 11 Jost, Jürgen 11 Lawrie, Andrew G. W. 11 Murphy, Jason 11 Nguyen, Van Tien 10 Cazenave, Thierry 10 Cuccagna, Scipio 10 Kowalczyk, Michał 9 Carles, Rémi 9 Fibich, Gadi 9 Ghoul, Tej-Eddine 9 Hamza, Mohamed Ali 9 Jendrej, Jacek 9 Li, Dong 9 Miyamoto, Yasuhito 9 Pistoia, Angela 9 Yang, Kai 8 Colliander, James E. 8 Deng, Shengbing 8 Fang, Daoyuan 8 Gan, Zaihui 8 Gao, Yanfang 8 Grossi, Massimo 8 Guo, Zihua 8 Klein, Christian 8 Lei, Yutian 8 Lenzmann, Enno 8 Li, Xiaoguang 8 Liu, Yue 8 Maeda, Masaya 8 Masmoudi, Nader 8 Pausader, Benoît 8 Perelman, Galina 8 Struwe, Michael 8 Tao, Terence 8 Tzvetkov, Nikolay 8 Zhang, Lei 7 Banica, Valeria 7 Cheng, Xing 7 Cho, Yonggeun 7 Choe, Kwangseok 7 Collot, Charles 7 Forcella, Luigi 7 Galaktionov, Victor Aleksandrovich 7 Guo, Qing 7 Ishige, Kazuhiro 7 Keraani, Sahbi 7 Kikuchi, Hiroaki 7 Lucia, Marcello 7 Mizumachi, Tetsu 7 Nawa, Hayato 7 Pastor, Ademir 7 Ponce, Gustavo ...and 1,285 more Authors all top 5 Cited in 233 Serials 147 Journal of Differential Equations 93 Journal of Functional Analysis 76 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 76 Calculus of Variations and Partial Differential Equations 74 Communications in Mathematical Physics 74 Journal of Mathematical Analysis and Applications 64 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 60 Communications in Partial Differential Equations 52 Discrete and Continuous Dynamical Systems 49 Transactions of the American Mathematical Society 44 Journal of Mathematical Physics 37 Archive for Rational Mechanics and Analysis 35 Communications on Pure and Applied Analysis 33 Mathematische Annalen 25 Duke Mathematical Journal 25 Physica D 25 Journal de Mathématiques Pures et Appliquées. Neuvième Série 25 Communications in Contemporary Mathematics 23 Proceedings of the American Mathematical Society 23 SIAM Journal on Mathematical Analysis 22 Advances in Mathematics 22 Séminaire Laurent Schwartz. EDP et Applications 20 Nonlinearity 20 Acta Mathematica Sinica. 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Theory, Methods & Applications 8 Mathematical Methods in the Applied Sciences 8 Applied Mathematics and Computation 8 Revista Matemática Iberoamericana 8 The Journal of Geometric Analysis 8 Journal of Nonlinear Science 8 Advanced Nonlinear Studies 7 Applied Mathematics Letters 7 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 7 Geometric and Functional Analysis. GAFA 7 Bulletin des Sciences Mathématiques 7 Annales Henri Poincaré 7 Discrete and Continuous Dynamical Systems. Series B 6 Journal of Computational Physics 6 Mathematische Zeitschrift 6 Memoirs of the American Mathematical Society 6 Bulletin of the American Mathematical Society. New Series 6 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 6 Boundary Value Problems 6 Discrete and Continuous Dynamical Systems. Series S 5 Reviews in Mathematical Physics 5 Indiana University Mathematics Journal 5 Manuscripta Mathematica 5 Chinese Annals of Mathematics. Series B 5 Milan Journal of Mathematics 5 Advances in Nonlinear Analysis 4 Computers & Mathematics with Applications 4 Annales de l’Institut Fourier 4 Journal of Computational and Applied Mathematics 4 Journal of Inequalities and Applications 4 Annals of Mathematics. Second Series 4 Communications in Nonlinear Science and Numerical Simulation 4 Communications in Mathematics and Statistics 4 Journal of Elliptic and Parabolic Equations 3 Rocky Mountain Journal of Mathematics 3 Mathematics of Computation 3 Acta Mathematica 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Illinois Journal of Mathematics 3 Journal of the Korean Mathematical Society 3 Journal für die Reine und Angewandte Mathematik 3 Monatshefte für Mathematik 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Proceedings of the London Mathematical Society. Third Series 3 SIAM Journal on Numerical Analysis 3 Acta Applicandae Mathematicae 3 Asymptotic Analysis 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Potential Analysis 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 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 3 Evolution Equations and Control Theory 3 SN Partial Differential Equations and Applications 2 Journal of Statistical Physics ...and 133 more Serials all top 5 Cited in 47 Fields 1,765 Partial differential equations (35-XX) 130 Dynamical systems and ergodic theory (37-XX) 119 Global analysis, analysis on manifolds (58-XX) 118 Quantum theory (81-XX) 112 Fluid mechanics (76-XX) 84 Differential geometry (53-XX) 63 Numerical analysis (65-XX) 51 Operator theory (47-XX) 51 Statistical mechanics, structure of matter (82-XX) 45 Calculus of variations and optimal control; optimization (49-XX) 40 Functional analysis (46-XX) 35 Optics, electromagnetic theory (78-XX) 33 Ordinary differential equations (34-XX) 22 Harmonic analysis on Euclidean spaces (42-XX) 21 Biology and other natural sciences (92-XX) 19 Real functions (26-XX) 19 Mechanics of deformable solids (74-XX) 13 Probability theory and stochastic processes (60-XX) 12 Functions of a complex variable (30-XX) 11 Mechanics of particles and systems (70-XX) 11 Relativity and gravitational theory (83-XX) 9 Systems theory; control (93-XX) 8 Integral equations (45-XX) 7 Potential theory (31-XX) 6 Astronomy and astrophysics (85-XX) 5 Special functions (33-XX) 5 Difference and functional equations (39-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Statistics (62-XX) 2 History and biography (01-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Nonassociative rings and algebras (17-XX) 2 Measure and integration (28-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-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 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-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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