Edit Profile (opens in new tab) Merle, Frank Compute Distance To: Compute Author ID: merle.frank Published as: Merle, Frank; Merle, F.; Merle, Franck more...less Homepage: https://www.ihes.fr/en/professeur/frank-merle-2/ External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru · dblp · IdRef · theses.fr Documents Indexed: 159 Publications since 1987 4 Contributions as Editor Co-Authors: 33 Co-Authors with 137 Joint Publications 1,175 Co-Co-Authors all top 5 Co-Authors 26 single-authored 35 Martel, Yvan 28 Raphael, Pierre 24 Kenig, Carlos Eduardo 23 Zaag, Hatem 20 Duyckaerts, Thomas 9 Szeftel, Jérémie 6 Rodnianski, Igor 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 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 Nakanishi, Kenji 1 Roudenko, Svetlana 1 Serrin, James all top 5 Serials 16 Communications in Mathematical Physics 9 IMRN. International Mathematics Research Notices 9 Comptes Rendus de l’Académie des Sciences. Série I 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 5 Annals of Mathematics. Second Series 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 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 161 Partial differential equations (35-XX) 22 Dynamical systems and ergodic theory (37-XX) 8 Fluid mechanics (76-XX) 3 General and overarching topics; collections (00-XX) 3 Ordinary differential equations (34-XX) 3 Quantum theory (81-XX) 2 History and biography (01-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 138 Publications have been cited 5,267 times in 2,008 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 382 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 361 2006 Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202Kenig, Carlos E.; Merle, Frank 224 2008 The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263Merle, Frank; Raphaël, Pierre 143 2005 Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Zbl 0808.35141Merle, F. 117 1993 On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110Merle, Frank; Raphaël, Pierre 110 2004 Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity. Zbl 0707.35021Merle, Frank 104 1990 Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098Martel, Yvan; Merle, Frank; Tsai, Tai-Peng 95 2002 Compactness at blow-up time for \(L^2\) solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126Merle, F.; Vega, L. 90 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 89 2006 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 86 2011 L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. Zbl 0722.35047Merle, Frank; Tsutsumi, Yoshio 84 1990 On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098Matano, Hiroshi; Merle, Frank 84 2004 Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135Merle, Frank; Raphaël, Pierre 82 2003 Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 81 2013 Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137Merle, Frank; Raphaël, Pierre 80 2005 Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073Martel, Yvan; Merle, Frank 78 2001 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 78 1997 Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128Merle, Frank 70 2001 A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058Martel, Yvan; Merle, Frank 68 2000 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 68 2002 Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071Martel, Y.; Merle, F. 64 2001 Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150Duyckaerts, Thomas; Merle, Frank 63 2009 Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171Martel, Yvan; Merle, Frank 61 2005 Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093Martel, Yvan; Merle, Frank 61 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 60 2006 Scattering for \(\dot {H}^{1/2}\) bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180Kenig, Carlos E.; Merle, Frank 57 2010 Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084Matano, Hiroshi; Merle, Frank 57 2009 Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 57 2012 Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043Duyckaerts, Thomas; Merle, Frank 56 2008 Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234Côte, Raphaël; Martel, Yvan; Merle, Frank 55 2011 Existence of stationary states for nonlinear Dirac equations. Zbl 0696.35154Merle, F. 55 1988 Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081Martel, Yvan; Merle, Frank 55 2002 Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\). Zbl 0809.35019Brézis, Haïm; Merle, Frank; Rivière, Tristan 54 1994 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 54 2012 Solution of a nonlinear heat equation with arbitrarily given blow-up points. Zbl 0785.35012Merle, Frank 53 1992 Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 51 2013 A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086Merle, Frank; Zaag, Hatem 49 2000 Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043Merle, Frank; Zaag, Hatem 46 2003 Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136Kenig, Carlos E.; Merle, Frank 45 2011 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 44 1992 Existence of excited states for a nonlinear Dirac field. Zbl 0696.35158Balabane, Mikhael; Cazenave, Thierry; Douady, Adrien; Merle, Frank 44 1988 Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055Merle, Frank; Zaag, Hatem 43 2005 Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070Merle, Frank; Zaag, Hatem 42 2007 Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1252.35204Merle, Frank; Zaag, Hatem 41 2012 Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044Merle, Frank; Zaag, Hatem 41 1998 Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068Martel, Yvan; Merle, Frank 41 2008 Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Zbl 0808.35137Glangetas, L.; Merle, F. 41 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 40 1996 Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137Martel, Yvan; Merle, Frank; Raphaël, Pierre 39 2014 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 38 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 Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 35 2014 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 On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Zbl 1315.35134Merle, Frank; Zaag, Hatem 33 2015 Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024Merle, F.; Zaag, H. 32 1998 Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045Martel, Yvan; Merle, Frank 32 2011 Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307Martel, Yvan; Merle, Frank; Raphaël, Pierre 31 2015 Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088Matano, Hiroshi; Merle, Frank 30 2011 \(L^2\) stability of solitons for KdV equation. Zbl 1022.35061Merle, F.; Vega, L. 30 2003 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 29 2006 Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320Martel, Yvan; Merle, Frank; Raphaël, Pierre 29 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 Positive solutions of elliptic equations involving supercritical growth. Zbl 0742.35025Merle, F.; Peletier, L. A. 28 1991 Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178Collot, Charles; Merle, Frank; Raphaël, Pierre 28 2017 Blow-up results of virial type for Zakharov equations. Zbl 0858.35117Merle, Frank 27 1996 Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182Merle, Frank; Raphaël, Pierre 26 2008 Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320Merle, Frank; Zaag, Hatem 26 2012 Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102Martel, Yvan; Merle, Frank 25 2002 Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121Martel, Yvan; Merle, Frank 24 2011 Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 23 2016 Type II blow up for the energy supercritical NLS. Zbl 1347.35215Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 22 2015 Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291Martel, Yvan; Merle, Frank 22 2009 Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090Antonini, Christophe; Merle, Frank 22 2001 The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 21 2013 On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478Merle, Frank; Zaag, Hatem 21 2005 Limit of the solution of a nonlinear Schrödinger equation at blow-up time. Zbl 0681.35078Merle, F. 20 1989 Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 20 2010 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 19 2011 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 Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Zbl 1339.35062Merle, Frank; Zaag, Hatem 18 2016 Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119Kenig, Carlos E.; Merle, Frank 18 2011 Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126Merle, Frank; Zaag, Hatem 18 2011 Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166Martel, Yvan; Merle, Frank 17 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. 17 1992 Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre 17 2016 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 17 2008 Self-focusing on bounded domains. Zbl 0980.35154Fibich, Gadi; Merle, Frank 16 2001 On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 14 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 13 1997 Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062Martel, Yvan; Merle, Frank 13 2008 Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253Collot, Charles; Merle, Frank; Raphaël, Pierre 12 2020 Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 12 2016 Modulation theory for the blowup of vector-valued nonlinear heat equations. Zbl 0814.35043Filippas, Stathis; Merle, Frank 12 1995 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 Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267Martel, Yvan; Merle, Frank; Mizumachi, Tetsu 10 2010 On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075Merle, Frank; Raphael, Pierre 9 2005 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 blow up for the energy super critical defocusing nonlinear Schrödinger equations. Zbl 1487.35353Merle, Frank; Raphaël, Pierre; Rodnianski, Igor; Szeftel, Jeremie 8 2022 On the implosion of a compressible fluid. II: Singularity formation. Zbl 1497.35385Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie 3 2022 On the implosion of a compressible fluid. I: Smooth self-similar inviscid profiles. Zbl 1497.35384Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie 2 2022 Soliton resolution for critical co-rotational wave maps and radial cubic wave equation. Zbl 1491.35292Duyckaerts, Thomas; Kenig, Carlos; Martel, Yvan; Merle, Frank 1 2022 Decay estimates for nonradiative solutions of the energy-critical focusing wave equation. Zbl 1472.35050Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 2 2021 Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253Collot, Charles; Merle, Frank; Raphaël, Pierre 12 2020 On strongly anisotropic type I blowup. Zbl 1432.35124Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 8 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 7 2019 Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111Martel, Yvan; Merle, Frank 4 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 2 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 28 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 7 2017 Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 23 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 18 2016 Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166Martel, Yvan; Merle, Frank 17 2016 Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre 17 2016 Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 12 2016 Global existence for solutions of the focusing wave equation with the compactness property. Zbl 1362.35190Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 2 2016 On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Zbl 1315.35134Merle, Frank; Zaag, Hatem 33 2015 Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307Martel, Yvan; Merle, Frank; Raphaël, Pierre 31 2015 Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320Martel, Yvan; Merle, Frank; Raphaël, Pierre 29 2015 Type II blow up for the energy supercritical NLS. Zbl 1347.35215Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 22 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 39 2014 Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 35 2014 On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 14 2014 Near soliton dynamics and singularity formation for \( L^2\) critical problems. Zbl 1304.35650Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J. 5 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 81 2013 Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 51 2013 The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 21 2013 Blow up and near soliton dynamics for the \(L^2\) critical gKdV equation. Zbl 1319.35224Martel, Yvan; Merle, Frank; Raphaël, Pierre 5 2013 Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 57 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 54 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 41 2012 Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320Merle, Frank; Zaag, Hatem 26 2012 Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1280.35019Merle, Frank 2 2012 Two blow-up regimes for \(L^2\). Zbl 1280.35140Merle, Frank; Raphaël, Pierre; Szeftel, Jérémie 1 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 86 2011 Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234Côte, Raphaël; Martel, Yvan; Merle, Frank 55 2011 Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136Kenig, Carlos E.; Merle, Frank 45 2011 Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045Martel, Yvan; Merle, Frank 32 2011 Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088Matano, Hiroshi; Merle, Frank 30 2011 Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121Martel, Yvan; Merle, Frank 24 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 19 2011 Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119Kenig, Carlos E.; Merle, Frank 18 2011 Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126Merle, Frank; Zaag, Hatem 18 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 57 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 10 2010 Inelastic interaction of nearly equal solitons for the BBM equation. Zbl 1188.35165Martel, Yvan; Merle, Frank 5 2010 Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150Duyckaerts, Thomas; Merle, Frank 63 2009 Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084Matano, Hiroshi; Merle, Frank 57 2009 Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291Martel, Yvan; Merle, Frank 22 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 224 2008 Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043Duyckaerts, Thomas; Merle, Frank 56 2008 Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068Martel, Yvan; Merle, Frank 41 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 38 2008 Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182Merle, Frank; Raphaël, Pierre 26 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 17 2008 Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062Martel, Yvan; Merle, Frank 13 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 42 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 361 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 89 2006 Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093Martel, Yvan; Merle, Frank 61 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 60 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 29 2006 Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders. Zbl 1105.35051Kenig, Carlos E.; Merle, Frank 6 2006 The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263Merle, Frank; Raphaël, Pierre 143 2005 Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137Merle, Frank; Raphaël, Pierre 80 2005 Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171Martel, Yvan; Merle, Frank 61 2005 Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055Merle, Frank; Zaag, Hatem 43 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 9 2005 On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110Merle, Frank; Raphaël, Pierre 110 2004 On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098Matano, Hiroshi; Merle, Frank 84 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 82 2003 Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043Merle, Frank; Zaag, Hatem 46 2003 \(L^2\) stability of solitons for KdV equation. Zbl 1022.35061Merle, F.; Vega, L. 30 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 95 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 68 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 55 2002 Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102Martel, Yvan; Merle, Frank 25 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 78 2001 Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128Merle, Frank 70 2001 Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071Martel, Y.; Merle, F. 64 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 16 2001 Uniform blow-up estimates for nonlinear heat equations and applications. Zbl 1019.35044Merle, Frank; Zaag, Hatem 1 2001 ...and 38 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,493 Authors 73 Merle, Frank 45 Martel, Yvan 45 Zaag, Hatem 44 Wei, Juncheng 40 Raphael, Pierre 34 Kenig, Carlos Eduardo 32 Bartolucci, Daniele 31 Lin, Chang-Shou 28 Muñoz, Claudio 25 Musso, Monica 24 Krieger, Joachim 24 Zhang, Jian 22 Saanouni, Tarek 21 Duyckaerts, Thomas 20 Roudenko, Svetlana 20 Zhu, Shihui 19 Miao, Changxing 19 Nakanishi, Kenji 19 Zhao, Lifeng 18 Côte, Raphaël 18 Del Pino, Manuel A. 18 Ding, Yanheng 18 Schlag, Wilhelm 17 Donninger, Roland 17 Mizoguchi, Noriko 17 Souplet, Philippe 17 Tarantello, Gabriella 17 Zheng, Jiqiang 16 Holmer, Justin 16 Yang, Wen 16 Zhou, Chunqin 15 Dinh, Van Duong 15 Dodson, Benjamin G. 15 Guo, Boling 15 Lee, Youngae 15 Martinazzi, Luca 15 Visan, Monica 14 Farah, Luiz Gustavo 14 Lawrie, Andrew G. W. 14 Malchiodi, Andrea 14 Tataru, Daniel 13 Cuccagna, Scipio 13 Ghoul, Tej-Eddine 13 Jevnikar, Aleks Yang Wen 13 Murphy, Jason 13 Suzuki, Takashi 13 Xu, Guixiang 13 Zhang, Xiaoyi 12 Ibrahim, Slim 12 Killip, Rowan 12 Kowalczyk, Michał 12 Nguyen, Van Tien 12 Wang, Guofang 12 Yang, Kai 11 Bahouri, Hajer 11 Jost, Jürgen 11 Maeda, Masaya 11 Masmoudi, Nader 11 Miyamoto, Yasuhito 10 Cazenave, Thierry 10 Jendrej, Jacek 10 Liu, Yue 10 Zhang, Lei 9 Carles, Rémi 9 Collot, Charles 9 Fibich, Gadi 9 Guzmán, Carlos M. 9 Hamza, Mohamed Ali 9 Li, Dong 9 Pastor, Ademir 9 Pistoia, Angela 9 Szeftel, Jérémie 9 Tzvetkov, Nikolay 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 Pausader, Benoît 8 Perelman, Galina 8 Struwe, Michael 8 Tao, Terence 8 Visciglia, Nicola 8 Wang, Zhong 8 Zhang, Jian 8 Zhao, Zehua 7 Akahori, Takafumi 7 Banica, Valeria 7 Cheng, Xing 7 Cho, Yonggeun 7 Choe, Kwangseok 7 D’Aprile, Teresa 7 Forcella, Luigi 7 Galaktionov, Victor Aleksandrovich ...and 1,393 more Authors all top 5 Cited in 249 Serials 151 Journal of Differential Equations 99 Journal of Functional Analysis 84 Calculus of Variations and Partial Differential Equations 82 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 78 Journal of Mathematical Analysis and Applications 77 Communications in Mathematical Physics 65 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 62 Communications in Partial Differential Equations 54 Discrete and Continuous Dynamical Systems 51 Transactions of the American Mathematical Society 48 Journal of Mathematical Physics 41 Archive for Rational Mechanics and Analysis 36 Communications on Pure and Applied Analysis 33 Mathematische Annalen 29 Journal de Mathématiques Pures et Appliquées. Neuvième Série 27 Physica D 26 Communications in Contemporary Mathematics 25 Duke Mathematical Journal 24 Proceedings of the American Mathematical Society 24 SIAM Journal on Mathematical Analysis 24 Séminaire Laurent Schwartz. EDP et Applications 23 Advances in Mathematics 21 Acta Mathematica Sinica. English Series 20 Nonlinearity 20 Inventiones Mathematicae 19 NoDEA. 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Series B 5 Asymptotic Analysis 5 Communications in Nonlinear Science and Numerical Simulation 5 Milan Journal of Mathematics 4 Computers & Mathematics with Applications 4 Annales de l’Institut Fourier 4 Bulletin de la Société Mathématique de France 4 Journal of Computational and Applied Mathematics 4 SIAM Journal on Numerical Analysis 4 SIAM Journal on Scientific Computing 4 Journal of Inequalities and Applications 4 Communications in Mathematics and Statistics 4 Journal of Elliptic and Parabolic Equations 4 SN Partial Differential Equations and Applications 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 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Illinois Journal of Mathematics 3 Journal of the Korean Mathematical Society 3 Journal für die Reine und Angewandte Mathematik 3 Pacific Journal of Mathematics 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Proceedings of the London Mathematical Society. Third Series 3 Acta Applicandae Mathematicae 3 Applied Numerical Mathematics 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 ...and 149 more Serials all top 5 Cited in 46 Fields 1,911 Partial differential equations (35-XX) 145 Dynamical systems and ergodic theory (37-XX) 132 Quantum theory (81-XX) 128 Fluid mechanics (76-XX) 126 Global analysis, analysis on manifolds (58-XX) 86 Differential geometry (53-XX) 71 Numerical analysis (65-XX) 59 Operator theory (47-XX) 55 Statistical mechanics, structure of matter (82-XX) 49 Calculus of variations and optimal control; optimization (49-XX) 42 Functional analysis (46-XX) 38 Ordinary differential equations (34-XX) 38 Optics, electromagnetic theory (78-XX) 27 Harmonic analysis on Euclidean spaces (42-XX) 24 Biology and other natural sciences (92-XX) 21 Real functions (26-XX) 20 Mechanics of deformable solids (74-XX) 14 Functions of a complex variable (30-XX) 13 Probability theory and stochastic processes (60-XX) 12 Potential theory (31-XX) 12 Mechanics of particles and systems (70-XX) 12 Relativity and gravitational theory (83-XX) 10 Systems theory; control (93-XX) 9 Astronomy and astrophysics (85-XX) 8 Integral equations (45-XX) 5 Special functions (33-XX) 4 Difference and functional equations (39-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Measure and integration (28-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 Group theory and generalizations (20-XX) 2 Abstract harmonic analysis (43-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 Topological groups, Lie groups (22-XX) 1 Approximations and expansions (41-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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