Edit Profile (opens in new tab) Merle, Frank Co-Author Distance 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 Videos: carmin.tv Documents Indexed: 167 Publications since 1987, including 4 Additional arXiv Preprints 4 Contributions as Editor Biographic References: 1 Publication Co-Authors: 35 Co-Authors with 145 Joint Publications 1,312 Co-Co-Authors all top 5 Co-Authors 26 single-authored 35 Martel, Yvan 30 Raphael, Pierre 28 Kenig, Carlos Eduardo 24 Duyckaerts, Thomas 24 Zaag, Hatem 11 Szeftel, Jérémie 8 Rodnianski, Igor 6 Collot, Charles 5 Peletier, Lambertus Adrianus 4 Berestycki, Henri 4 Hilhorst, Danielle 4 Mimura, Masayasu 4 Pakdaman, Khashayar 3 Brézis, Haïm 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 Jia, Hao 2 Rivière, Tristan 2 Tsai, Tai-Peng 2 Tsutsumi, Yoshio 2 Vega, Luis 1 Antonini, Christophe 1 Fermanian-Kammerer, Clotilde 1 Kim, Kihyun 1 Mizumachi, Tetsu 1 Nakanishi, Kenji 1 Roudenko, Svetlana 1 Serrin, James all top 5 Serials 16 Communications in Mathematical Physics 10 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 Acta Mathematica 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 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 Advances in Mathematics 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 Vietnam Journal of Mathematics 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 169 Partial differential equations (35-XX) 23 Dynamical systems and ergodic theory (37-XX) 8 Fluid mechanics (76-XX) 4 Ordinary differential equations (34-XX) 4 Quantum theory (81-XX) 3 General and overarching topics; collections (00-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 History and biography (01-XX) 1 Operator theory (47-XX) 1 Optics, electromagnetic theory (78-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 147 Publications have been cited 6,607 times in 2,520 Documents Cited by ▼ Year ▼ Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrödinger equation in the radial case. Zbl 1115.35125 Kenig, Carlos E.; Merle, Frank 446 2006 Uniform estimates and blow-up behavior for solutions of \(-\Delta{} u =V(x) e^ u\) in two dimensions. Zbl 0746.35006 Brézis, Haïm; Merle, Frank 431 1991 Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202 Kenig, Carlos E.; Merle, Frank 259 2008 The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263 Merle, Frank; Raphaël, Pierre 186 2005 Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power. Zbl 0808.35141 Merle, F. 147 1993 On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110 Merle, Frank; Raphaël, Pierre 134 2004 Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity. Zbl 0707.35021 Merle, Frank 122 1990 Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098 Martel, Yvan; Merle, Frank; Tsai, Tai-Peng 121 2002 On a sharp lower bound on the blow-up rate for the \(L^2\) critical nonlinear Schrödinger equation. Zbl 1075.35077 Merle, Frank; Raphaël, Pierre 114 2006 Asymptotic stability of solitons for subcritical generalized KdV equations. Zbl 0981.35073 Martel, Yvan; Merle, Frank 106 2001 Compactness at blow-up time for \(L^2\) solutions of the critical nonlinear Schrödinger equation in 2D. Zbl 0913.35126 Merle, F.; Vega, L. 105 1998 Stability of the blow-up profile for equations of the type \(u_ t=\Delta u+| u| ^{p-1}u\). Zbl 0872.35049 Merle, Frank; Zaag, Hatem 103 1997 Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 100 2013 Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135 Merle, Frank; Raphaël, Pierre 100 2003 L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity. Zbl 0722.35047 Merle, Frank; Tsutsumi, Yoshio 97 1990 Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137 Merle, Frank; Raphaël, Pierre 97 2005 On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098 Matano, Hiroshi; Merle, Frank 95 2004 Optimal estimates for blowup rate and behavior for nonlinear heat equations. Zbl 0899.35044 Merle, Frank; Zaag, Hatem 87 1998 Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation. Zbl 1230.35067 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 86 2011 Existence of blow-up solutions in the energy space for the critical generalized KdV equation. Zbl 0970.35128 Merle, Frank 85 2001 A Liouville theorem for the critical generalized Korteweg-de Vries equation. Zbl 0963.37058 Martel, Yvan; Merle, Frank 82 2000 Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171 Martel, Yvan; Merle, Frank 78 2005 Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093 Martel, Yvan; Merle, Frank 77 2006 Blow up in finite time and dynamics of blow up solutions for the \(L^2\)-critical generalized KdV equation. Zbl 0996.35064 Martel, Yvan; Merle, Frank 76 2002 Instability of solitons for the critical generalized Korteweg-de Vries equation. Zbl 0985.35071 Martel, Y.; Merle, F. 74 2001 Scattering for \(\dot {H}^{1/2}\) bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180 Kenig, Carlos E.; Merle, Frank 74 2010 Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150 Duyckaerts, Thomas; Merle, Frank 73 2009 Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052 Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 73 2013 Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations. Zbl 1099.35134 Martel, Yvan; Merle, Frank; Tsai, Tai-Peng 71 2006 Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234 Côte, Raphaël; Martel, Yvan; Merle, Frank 69 2011 Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084 Matano, Hiroshi; Merle, Frank 68 2009 Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043 Duyckaerts, Thomas; Merle, Frank 66 2008 Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081 Martel, Yvan; Merle, Frank 66 2002 Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137 Martel, Yvan; Merle, Frank; Raphaël, Pierre 66 2014 Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\). Zbl 0809.35019 Brézis, Haïm; Merle, Frank; Rivière, Tristan 63 1994 Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. Zbl 1282.35088 Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 63 2012 Nonexistence of minimal blow-up solutions of equations \(iu_ t = -\Delta u - k(x)| u|^{4/N} u\) in \(\mathbb{R}^ N\). Zbl 0846.35129 Merle, Franck 62 1996 Existence of stationary states for nonlinear Dirac equations. Zbl 0696.35154 Merle, F. 61 1988 Solution of a nonlinear heat equation with arbitrarily given blow-up points. Zbl 0785.35012 Merle, Frank 57 1992 Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 56 2012 Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068 Martel, Yvan; Merle, Frank 55 2008 Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043 Merle, Frank; Zaag, Hatem 53 2003 A Liouville theorem for vector-valued nonlinear heat equations and applications. Zbl 0939.35086 Merle, Frank; Zaag, Hatem 52 2000 Soliton resolution along a sequence of times for the focusing energy critical wave equation. Zbl 1391.35276 Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank 52 2017 Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136 Kenig, Carlos E.; Merle, Frank 51 2011 Existence of excited states for a nonlinear Dirac field. Zbl 0696.35158 Balabane, Mikhael; Cazenave, Thierry; Douady, Adrien; Merle, Frank 50 1988 Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070 Merle, Frank; Zaag, Hatem 50 2007 Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055 Merle, Frank; Zaag, Hatem 49 2005 On uniqueness and continuation properties after blow-up time of self- similar solutions of nonlinear Schrödinger equation with critical exponent and critical mass. Zbl 0767.35084 Merle, Frank 48 1992 Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Zbl 0808.35137 Glangetas, L.; Merle, F. 47 1994 Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1252.35204 Merle, Frank; Zaag, Hatem 46 2012 Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045 Martel, Yvan; Merle, Frank 44 2011 Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320 Martel, Yvan; Merle, Frank; Raphaël, Pierre 42 2015 On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Zbl 1315.35134 Merle, Frank; Zaag, Hatem 42 2015 Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 41 2014 Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation. Zbl 1159.35046 Merle, Frank; Zaag, Hatem 40 2008 Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307 Martel, Yvan; Merle, Frank; Raphaël, Pierre 40 2015 Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182 Merle, Frank; Raphaël, Pierre 38 2008 \(L^2\) stability of solitons for KdV equation. Zbl 1022.35061 Merle, F.; Vega, L. 38 2003 Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II. Zbl 0808.35138 Glangetas, L.; Merle, F. 37 1994 Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178 Collot, Charles; Merle, Frank; Raphaël, Pierre 37 2017 Blow-up results of virial type for Zakharov equations. Zbl 0858.35117 Merle, Frank 36 1996 Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121 Martel, Yvan; Merle, Frank 36 2011 Refined uniform estimates at blow-up and applications for nonlinear heat equations. Zbl 0926.35024 Merle, F.; Zaag, H. 35 1998 Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088 Matano, Hiroshi; Merle, Frank 35 2011 Positive solutions of elliptic equations involving supercritical growth. Zbl 0742.35025 Merle, F.; Peletier, L. A. 34 1991 On the implosion of a compressible fluid. II: Singularity formation. Zbl 1497.35385 Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie 34 2022 The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145 Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 33 2013 Proof of a spectral property related to the singularity formation for the \(L^{2}\) critical nonlinear Schrödinger equation. Zbl 1100.35097 Fibich, Gadi; Merle, Frank; Raphaël, Pierre 33 2006 Stability of the blow-up profile of nonlinear heat equations from the dynamical system point of view. Zbl 0971.35038 Fermanian Kammerer, C.; Merle, F.; Zaag, H. 32 2000 Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 30 2016 Type II blow up for the energy supercritical NLS. Zbl 1347.35215 Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 30 2015 On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478 Merle, Frank; Zaag, Hatem 29 2005 Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320 Merle, Frank; Zaag, Hatem 28 2012 Optimal bounds on positive blow-up solutions for a semilinear wave equation. Zbl 0989.35090 Antonini, Christophe; Merle, Frank 26 2001 On the implosion of a compressible fluid. I: Smooth self-similar inviscid profiles. Zbl 1497.35384 Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie 26 2022 Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291 Martel, Yvan; Merle, Frank 25 2009 Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102 Martel, Yvan; Merle, Frank 24 2002 On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Zbl 1487.35353 Merle, Frank; Raphaël, Pierre; Rodnianski, Igor; Szeftel, Jeremie 24 2022 Self-focusing on bounded domains. Zbl 0980.35154 Fibich, Gadi; Merle, Frank 23 2001 Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153 Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 23 2010 Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315 Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre 23 2016 On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283 Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 22 2014 Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system. Zbl 1170.35064 Côte, Raphaël; Kenig, Carlos E.; Merle, Frank 22 2008 Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. I: The radial case. Zbl 0719.35004 Merle, F.; Peletier, L. A. 20 1990 Limit of the solution of a nonlinear Schrödinger equation at blow-up time. Zbl 0681.35078 Merle, F. 20 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 1213.35139 Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 20 2011 Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Zbl 1339.35062 Merle, Frank; Zaag, Hatem 20 2016 Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126 Merle, Frank; Zaag, Hatem 19 2011 Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166 Martel, Yvan; Merle, Frank 19 2016 Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119 Kenig, Carlos E.; Merle, Frank 18 2011 Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253 Collot, Charles; Merle, Frank; Raphaël, Pierre 18 2020 Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. II: The nonradial case. Zbl 0771.35008 Merle, F.; Peletier, L. A. 17 1992 Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062 Martel, Yvan; Merle, Frank 16 2008 Lower bounds for the blowup rate of solutions of the Zakharov equation in dimension two. Zbl 0856.35014 Merle, Frank 15 1996 Reconnection of vortex with the boundary and finite time quenching. Zbl 0910.35020 Merle, Frank; Zaag, Hatem 15 1997 Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. Zbl 1320.35066 Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 14 2015 Scattering profile for global solutions of the energy-critical wave equation. Zbl 1437.35497 Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 14 2019 On strongly anisotropic type I blowup. Zbl 1432.35124 Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 14 2020 Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267 Martel, Yvan; Merle, Frank; Mizumachi, Tetsu 13 2010 Soliton resolution for the radial quadratic wave equation in space dimension 6. Zbl 1543.35111 Collot, Charles; Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 1 2024 Soliton resolution for the radial critical wave equation in all odd space dimensions. Zbl 1520.35103 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 10 2023 On classification of non-radiative solutions for various energy-critical wave equations. Zbl 1527.35180 Collot, Charles; Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 1 2023 On channels of energy for the radial linearised energy critical wave equation in the degenerate case. Zbl 1541.81031 Collot, Charles; Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 1 2023 On the implosion of a compressible fluid. II: Singularity formation. Zbl 1497.35385 Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie 34 2022 On the implosion of a compressible fluid. I: Smooth self-similar inviscid profiles. Zbl 1497.35384 Merle, Frank; Rapha\'’el, Pierre; Rodnianski, Igor; Szeftel, Jeremie 26 2022 On blow up for the energy super critical defocusing nonlinear Schrödinger equations. Zbl 1487.35353 Merle, Frank; Raphaël, Pierre; Rodnianski, Igor; Szeftel, Jeremie 24 2022 Soliton resolution for critical co-rotational wave maps and radial cubic wave equation. Zbl 1491.35292 Duyckaerts, Thomas; Kenig, Carlos; Martel, Yvan; Merle, Frank 13 2022 Behavior rigidity near non-isolated blow-up points for the semilinear heat equation. Zbl 1501.35092 Merle, Frank; Zaag, Hatem 2 2022 Decay estimates for nonradiative solutions of the energy-critical focusing wave equation. Zbl 1472.35050 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 10 2021 Strongly anisotropic type II blow up at an isolated point. Zbl 1436.35253 Collot, Charles; Merle, Frank; Raphaël, Pierre 18 2020 On strongly anisotropic type I blowup. Zbl 1432.35124 Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 14 2020 Exterior energy bounds for the critical wave equation close to the ground state. Zbl 1450.35157 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 10 2020 Scattering profile for global solutions of the energy-critical wave equation. Zbl 1437.35497 Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 14 2019 Inelasticity of soliton collisions for the 5D energy critical wave equation. Zbl 1408.76111 Martel, Yvan; Merle, Frank 10 2018 Universality of blow up profile for small blow up solutions to the energy critical wave map equation. Zbl 1421.35038 Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank 6 2018 Blowup solutions to the semilinear wave equation with a stylized pyramid as a blowup surface. Zbl 1402.35181 Merle, Frank; Zaag, Hatem 2 2018 Soliton resolution along a sequence of times for the focusing energy critical wave equation. Zbl 1391.35276 Duyckaerts, Thomas; Jia, Hao; Kenig, Carlos; Merle, Frank 52 2017 Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions. Zbl 1401.35178 Collot, Charles; Merle, Frank; Raphaël, Pierre 37 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 1364.35156 Collot, Charles; Merle, Frank; Raphaël, Pierre 8 2017 Solutions of the focusing nonradial critical wave equation with the compactness property. Zbl 1348.35141 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 30 2016 Codimension one threshold manifold for the critical gKdV equation. Zbl 1336.35315 Martel, Yvan; Merle, Frank; Nakanishi, Kenji; Raphaël, Pierre 23 2016 Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. Zbl 1339.35062 Merle, Frank; Zaag, Hatem 20 2016 Construction of multi-solitons for the energy-critical wave equation in dimension 5. Zbl 1359.35166 Martel, Yvan; Merle, Frank 19 2016 Concentration-compactness and universal profiles for the non-radial energy critical wave equation. Zbl 1339.35186 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 13 2016 Global existence for solutions of the focusing wave equation with the compactness property. Zbl 1362.35190 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 4 2016 Blow up for the critical gKdV equation. II: Minimal mass dynamics. Zbl 1326.35320 Martel, Yvan; Merle, Frank; Raphaël, Pierre 42 2015 On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations. Zbl 1315.35134 Merle, Frank; Zaag, Hatem 42 2015 Blow up for the critical gKdV equation. III: Exotic regimes. Zbl 1331.35307 Martel, Yvan; Merle, Frank; Raphaël, Pierre 40 2015 Type II blow up for the energy supercritical NLS. Zbl 1347.35215 Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 30 2015 Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations. Zbl 1320.35066 Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 14 2015 On the nonexistence of pure multi-solitons for the quartic gKdV equation. Zbl 1315.35191 Martel, Yvan; Merle, Frank 8 2015 Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton. Zbl 1301.35137 Martel, Yvan; Merle, Frank; Raphaël, Pierre 66 2014 Scattering for radial, bounded solutions of focusing supercritical wave equations. Zbl 1310.35171 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 41 2014 On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Zbl 1292.35283 Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 22 2014 Near soliton dynamics and singularity formation for \( L^2\) critical problems. Zbl 1304.35650 Martel, Y.; Merle, F.; Raphaël, P.; Szeftel, J. 6 2014 Asymptotics for critical nonlinear dispersive equations. Zbl 1373.35049 Merle, Frank 1 2014 Classification of the radial solutions of the focusing, energy-critical wave equation. Zbl 1308.35143 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 100 2013 Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem. Zbl 1326.35052 Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 73 2013 The instability of Bourgain-Wang solutions for the \(L^2\) critical NLS. Zbl 1294.35145 Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 33 2013 Blow up and near soliton dynamics for the \(L^2\) critical gKdV equation. Zbl 1319.35224 Martel, Yvan; Merle, Frank; Raphaël, Pierre 5 2013 Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. Zbl 1282.35088 Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank 63 2012 Profiles of bounded radial solutions of the focusing, energy-critical wave equation. Zbl 1258.35148 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 56 2012 Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1252.35204 Merle, Frank; Zaag, Hatem 46 2012 Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. Zbl 1270.35320 Merle, Frank; Zaag, Hatem 28 2012 Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension. Zbl 1280.35019 Merle, Frank 6 2012 Two blow-up regimes for \(L^2\). Zbl 1280.35140 Merle, 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 1230.35067 Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank 86 2011 Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations. Zbl 1273.35234 Côte, Raphaël; Martel, Yvan; Merle, Frank 69 2011 Nondispersive radial solutions to energy supercritical non-linear wave equations, with applications. Zbl 1241.35136 Kenig, Carlos E.; Merle, Frank 51 2011 Description of two soliton collision for the quartic gKdV equation. Zbl 1300.37045 Martel, Yvan; Merle, Frank 44 2011 Inelastic interaction of nearly equal solitons for the quartic gKdV equation. Zbl 1230.35121 Martel, Yvan; Merle, Frank 36 2011 Threshold and generic type I behaviors for a supercritical nonlinear heat equation. Zbl 1223.35088 Matano, Hiroshi; Merle, Frank 35 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 1213.35139 Merle, Frank; Raphaël, Pierre; Rodnianski, Igor 20 2011 Blow-up behavior outside the origin for a semilinear wave equation in the radial case. Zbl 1222.35126 Merle, Frank; Zaag, Hatem 19 2011 Radial solutions to energy supercritical wave equations in odd dimensions. Zbl 1298.35119 Kenig, Carlos E.; Merle, Frank 18 2011 Maximizers for the Strichartz norm for small solutions of mass-critical NLS. Zbl 1247.35142 Duyckaerts, Thomas; Merle, Frank; Roudenko, Svetlana 8 2011 Review of long time asymptotics and collision of solitons for the quartic generalized Korteweg-de Vries equation. Zbl 1219.35248 Martel, Yvan; Merle, Frank 7 2011 Scattering for \(\dot {H}^{1/2}\) bounded solutions to the cubic, defocusing NLS in 3 dimensions. Zbl 1188.35180 Kenig, Carlos E.; Merle, Frank 74 2010 Stable self-similar blow-up dynamics for slightly \(L^{2}\) super-critical NLS equations. Zbl 1204.35153 Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie 23 2010 Description of the inelastic collision of two solitary waves for the BBM equation. Zbl 1200.35267 Martel, Yvan; Merle, Frank; Mizumachi, Tetsu 13 2010 Inelastic interaction of nearly equal solitons for the BBM equation. Zbl 1188.35165 Martel, Yvan; Merle, Frank 7 2010 Dynamic of threshold solutions for energy-critical NLS. Zbl 1232.35150 Duyckaerts, Thomas; Merle, Frank 73 2009 Classification of type I and type II behaviors for a supercritical nonlinear heat equation. Zbl 1178.35084 Matano, Hiroshi; Merle, Frank 68 2009 Stability of two soliton collision for nonintegrable gKdV equations. Zbl 1179.35291 Martel, Yvan; Merle, Frank 25 2009 Scattering norm estimate near the threshold for energy-critical focusing semilinear wave equation. Zbl 1179.35189 Duyckaerts, Thomas; Merle, Frank 1 2009 Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Zbl 1183.35202 Kenig, Carlos E.; Merle, Frank 259 2008 Dynamics of threshold solutions for energy-critical wave equation. Zbl 1159.35043 Duyckaerts, Thomas; Merle, Frank 66 2008 Asymptotic stability of solitons of the gKdV equations with general nonlinearity. Zbl 1153.35068 Martel, Yvan; Merle, Frank 55 2008 Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation. Zbl 1159.35046 Merle, Frank; Zaag, Hatem 40 2008 Blow up of the critical norm for some radial \(L^2\) super critical nonlinear Schrödinger equations. Zbl 1188.35182 Merle, Frank; Raphaël, Pierre 38 2008 Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system. Zbl 1170.35064 Côte, Raphaël; Kenig, Carlos E.; Merle, Frank 22 2008 Refined asymptotics around solitons for gKdV equations. Zbl 1137.35062 Martel, Yvan; Merle, Frank 16 2008 Note on coupled linear systems related to two soliton collision for the quartic gKdV equation. Zbl 1188.35164 Martel, Yvan; Merle, Frank 5 2008 Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. Zbl 1133.35070 Merle, Frank; Zaag, Hatem 50 2007 Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrödinger equation in the radial case. Zbl 1115.35125 Kenig, Carlos E.; Merle, Frank 446 2006 On a sharp lower bound on the blow-up rate for the \(L^2\) critical nonlinear Schrödinger equation. Zbl 1075.35077 Merle, Frank; Raphaël, Pierre 114 2006 Multi solitary waves for nonlinear Schrödinger equations. Zbl 1133.35093 Martel, Yvan; Merle, Frank 77 2006 Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations. Zbl 1099.35134 Martel, Yvan; Merle, Frank; Tsai, Tai-Peng 71 2006 Proof of a spectral property related to the singularity formation for the \(L^{2}\) critical nonlinear Schrödinger equation. Zbl 1100.35097 Fibich, Gadi; Merle, Frank; Raphaël, Pierre 33 2006 Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders. Zbl 1105.35051 Kenig, Carlos E.; Merle, Frank 6 2006 A note on a symmetry result for traveling waves in cylinders. Zbl 1085.35070 Kenig, C. E.; Merle, F. 1 2006 The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation. Zbl 1185.35263 Merle, Frank; Raphaël, Pierre 186 2005 Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation. Zbl 1062.35137 Merle, Frank; Raphaël, Pierre 97 2005 Asymptotic stability of solitons of the subcritical gKdV equations revisited. Zbl 1064.35171 Martel, Yvan; Merle, Frank 78 2005 Determination of the blow-up rate for a critical semilinear wave equation. Zbl 1136.35055 Merle, Frank; Zaag, Hatem 49 2005 On growth rate near the blowup surface for semilinear wave equations. Zbl 1160.35478 Merle, Frank; Zaag, Hatem 29 2005 On one blow up point solutions to the critical nonlinear Schrödinger equation. Zbl 1117.35075 Merle, Frank; Raphael, Pierre 9 2005 On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation. Zbl 1067.35110 Merle, Frank; Raphaël, Pierre 134 2004 On nonexistence of type II blowup for a supercritical nonlinear heat equation. Zbl 1112.35098 Matano, Hiroshi; Merle, Frank 95 2004 Review on blow up and asymptotic dynamics for critical and subcritical gKdV equations. Zbl 1071.35114 Martel, Yvan; Merle, Frank 3 2004 Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation. Zbl 1061.35135 Merle, Frank; Raphaël, Pierre 100 2003 Determination of the blow-up rate for the semilinear wave equation. Zbl 1052.35043 Merle, Frank; Zaag, Hatem 53 2003 \(L^2\) stability of solitons for KdV equation. Zbl 1022.35061 Merle, F.; Vega, L. 38 2003 Qualitative results on the generalized critical KdV equation. Zbl 1044.35074 Martel, Yvan; Merle, Frank 1 2003 Stability and asymptotic stability for subcritical gKdV equations. Zbl 1017.35098 Martel, Yvan; Merle, Frank; Tsai, Tai-Peng 121 2002 Blow up in finite time and dynamics of blow up solutions for the \(L^2\)-critical generalized KdV equation. Zbl 0996.35064 Martel, Yvan; Merle, Frank 76 2002 Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation. Zbl 1005.35081 Martel, Yvan; Merle, Frank 66 2002 Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation. Zbl 1033.35102 Martel, Yvan; Merle, Frank 24 2002 O. D. E. type behavior of blow-up solutions of nonlinear heat equations. Zbl 1009.35039 Merle, Frank; Zaag, Hatem 10 2002 ...and 47 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,874 Authors 76 Merle, Frank 55 Zaag, Hatem 51 Wei, Juncheng 49 Martel, Yvan 42 Raphael, Pierre 40 Kenig, Carlos Eduardo 39 Saanouni, Tarek 33 Lin, Chang-Shou 32 Bartolucci, Daniele 32 Muñoz, Claudio 26 Musso, Monica 26 Zhang, Jian 25 Duyckaerts, Thomas 25 Krieger, Joachim 24 Roudenko, Svetlana 23 Miao, Changxing 22 Côte, Raphaël 22 Dinh, Van Duong 22 Zhu, Shihui 21 Zhao, Lifeng 20 Ding, Yanheng 20 Lawrie, Andrew G. W. 20 Nakanishi, Kenji 20 Souplet, Philippe 20 Tarantello, Gabriella 20 Zheng, Jiqiang 19 Dodson, Benjamin G. 19 Donninger, Roland 19 Mizoguchi, Noriko 19 Schlag, Wilhelm 18 Del Pino, Manuel A. 18 Farah, Luiz Gustavo 18 Murphy, Jason 18 Yang, Wen 17 Guo, Boling 17 Holmer, Justin 16 Ghoul, Tej-Eddine 16 Jevnikar, Aleks Yang Wen 16 Visan, Monica 16 Zhou, Chunqin 15 Jendrej, Jacek 15 Klein, Christian 15 Lee, Youngae 15 Malchiodi, Andrea 15 Tataru, Daniel 15 Xu, Guixiang 14 Collot, Charles 14 Cuccagna, Scipio 14 Nguyen, Van Tien 14 Suzuki, Takashi 14 Zhang, Xiaoyi 14 Zhao, Zehua 13 Ibrahim, Slim 13 Kowalczyk, Michał 13 Maeda, Masaya 13 Masmoudi, Nader 12 Killip, Rowan 12 Miyamoto, Yasuhito 12 Wang, Guofang 12 Zhang, Lei 11 Bahouri, Hajer 11 Carles, Rémi 11 Duong, Giao Ky 11 Guo, Zihua 11 Jost, Jürgen 11 Lei, Yutian 11 Nouaili, Nejla 11 Tzvetkov, Nikolay 10 Cazenave, Thierry 10 Fibich, Gadi 10 Guzmán, Carlos M. 10 Ikeda, Masahiro 10 Lenzmann, Enno 10 Liu, Yue 10 Masaki, Satoshi 10 Pistoia, Angela 10 Yang, Kai 10 Yang, Yunyan 9 Cheng, Xing 9 D’Aprile, Teresa 9 Deng, Shengbing 9 Feng, Binhua 9 Forcella, Luigi 9 Gan, Zaihui 9 Grossi, Massimo 9 Hyder, Ali 9 Inui, Takahisa 9 Li, Dong 9 Li, Ze 9 Lucia, Marcello 9 Martinazzi, Luca 9 Ogawa, Takayoshi 9 Pastor, Ademir 9 Perelman, Galina 9 Qu, Changzheng 9 Shen, Ruipeng 9 Su, Yiming 9 Szeftel, Jérémie 9 Visciglia, Nicola 9 Wang, Zhong ...and 1,774 more Authors all top 5 Cited in 283 Serials 184 Journal of Differential Equations 113 Journal of Functional Analysis 99 Calculus of Variations and Partial Differential Equations 94 Nonlinear Analysis. 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Series B 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 6 Bulletin of the American Mathematical Society. New Series 6 Annals of Mathematics. Second Series 5 Computers & Mathematics with Applications 5 Physics Letters. A 5 Reviews in Mathematical Physics 5 Manuscripta Mathematica 5 Mathematics and Computers in Simulation 5 SIAM Journal on Numerical Analysis 5 Applied Numerical Mathematics 5 Potential Analysis 5 Journal of Inequalities and Applications 5 Milan Journal of Mathematics 5 Journal of Fixed Point Theory and Applications 5 Pure and Applied Analysis 5 SN Partial Differential Equations and Applications 4 Wave Motion 4 Annales de l’Institut Fourier 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Bulletin de la Société Mathématique de France 4 Journal of Computational and Applied Mathematics 4 Journal für die Reine und Angewandte Mathematik 4 Mathematische Nachrichten 4 Quarterly of Applied Mathematics 4 Journal of Scientific Computing 4 SIAM Journal on Scientific Computing 4 Journal of Mathematical Fluid Mechanics 4 S\(\vec{\text{e}}\)MA Journal 4 Communications in Mathematics and Statistics 4 Evolution Equations and Control Theory 4 Journal of Elliptic and Parabolic Equations ...and 183 more Serials all top 5 Cited in 47 Fields 2,388 Partial differential equations (35-XX) 210 Dynamical systems and ergodic theory (37-XX) 185 Fluid mechanics (76-XX) 151 Global analysis, analysis on manifolds (58-XX) 151 Quantum theory (81-XX) 113 Differential geometry (53-XX) 98 Numerical analysis (65-XX) 69 Statistical mechanics, structure of matter (82-XX) 68 Operator theory (47-XX) 63 Calculus of variations and optimal control; optimization (49-XX) 56 Optics, electromagnetic theory (78-XX) 44 Functional analysis (46-XX) 43 Ordinary differential equations (34-XX) 41 Harmonic analysis on Euclidean spaces (42-XX) 30 Real functions (26-XX) 29 Biology and other natural sciences (92-XX) 27 Probability theory and stochastic processes (60-XX) 21 Mechanics of deformable solids (74-XX) 20 Functions of a complex variable (30-XX) 16 Systems theory; control (93-XX) 15 Potential theory (31-XX) 14 Relativity and gravitational theory (83-XX) 13 Astronomy and astrophysics (85-XX) 12 Integral equations (45-XX) 12 Mechanics of particles and systems (70-XX) 10 Classical thermodynamics, heat transfer (80-XX) 8 Several complex variables and analytic spaces (32-XX) 5 Nonassociative rings and algebras (17-XX) 5 Special functions (33-XX) 5 Difference and functional equations (39-XX) 4 Geophysics (86-XX) 3 General and overarching topics; collections (00-XX) 3 History and biography (01-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Measure and integration (28-XX) 3 Statistics (62-XX) 2 Algebraic geometry (14-XX) 2 Group theory and generalizations (20-XX) 2 Approximations and expansions (41-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 Computer science (68-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Topological groups, Lie groups (22-XX) 1 Manifolds and cell complexes (57-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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