Edit Profile (opens in new tab) Gerard, Patrick Co-Author Distance Author ID: gerard.patrick Published as: Gérard, Patrick; Gérard, P.; Gerard, Patrick; Gerard, P. more...less Homepage: https://www.imo.universite-paris-saclay.fr/~patrick.gerard/ External Links: MGP · Wikidata · dblp · GND · IdRef · theses.fr Videos: carmin.tv Member of Collective: Bourbaki, Nicolas Documents Indexed: 134 Publications since 1986, including 3 Books and 12 Additional arXiv Preprints Co-Authors: 42 Co-Authors with 100 Joint Publications 1,527 Co-Co-Authors all top 5 Co-Authors 29 single-authored 17 Burq, Nicolas 17 Tzvetkov, Nikolay 16 Grellier, Sandrine 9 Pushnitski, Alexander B. 8 Fermanian-Kammerer, Clotilde 8 Kappeler, Thomas 8 Topalov, Peter J. 6 Bahouri, Hajer 4 Lebeau, Gilles 4 Lenzmann, Enno 3 Blackstone, Elliot J. 3 Gassot, Louise 3 Leichtnam, Eric 3 Miller, Peter D. 2 Alinhac, Serge 2 Briane, Marc 2 Burg, Nocolas 2 Gallagher, Isabelle 2 Golse, François 2 Rauch, Jeffrey B. 2 Sanchez-Palencia, Évariste 2 Xu, Chao-Jiang 1 Bambusi, Dario 1 Biasi, Anxo 1 Brezzi, Franco 1 Dehman, Belhassen 1 Francfort, Gilles A. 1 Germain, Pierre 1 Guo, Yanqiu 1 He, Zihui 1 Klein, Christian 1 Koch, Herbert 1 Lasser, Caroline 1 Markowich, Peter Alexander 1 Mauser, Norbert Julius 1 Méhats, Florian 1 Meyer, Yves 1 Oru, Frédérique 1 Pallard, Christophe 1 Pierfelice, Vittoria 1 Pocovnicu, Oana 1 Poupaud, Frédéric 1 Raphael, Pierre 1 Thomann, Laurent 1 Titi, Edriss Saleh 1 Treil, Sergei 1 Wennberg, Bernt 1 Zhang, Zhifei all top 5 Serials 12 Séminaire Équations aux Dérivées Partielles 5 Séminaire Laurent Schwartz. EDP et Applications 4 Communications on Pure and Applied Mathematics 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Inventiones Mathematicae 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Archive for Rational Mechanics and Analysis 2 Journal d’Analyse Mathématique 2 American Journal of Mathematics 2 Bulletin de la Société Mathématique de France 2 Duke Mathematical Journal 2 Journal of Functional Analysis 2 Mathematische Zeitschrift 2 Communications in Partial Differential Equations 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 SIAM Journal on Mathematical Analysis 2 Mathematical Research Letters 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Tunisian Journal of Mathematics 1 Communications in Mathematical Physics 1 Letters in Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Nonlinearity 1 Studia Mathematica 1 Acta Mathematica 1 Annales de l’Institut Fourier 1 Gazette des Mathématiciens 1 Journal of the London Mathematical Society. Second Series 1 Mathematika 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Quarterly of Applied Mathematics 1 Transactions of the American Mathematical Society 1 Journal of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Annales Henri Poincaré 1 Journal of Nonlinear Mathematical Physics 1 Journal of the Institute of Mathematics of Jussieu 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Journal of Hyperbolic Differential Equations 1 Astérisque 1 Graduate Studies in Mathematics 1 Kinetic and Related Models 1 Analysis & PDE 1 Science China. Mathematics 1 Journal of Spectral Theory 1 Annals of PDE 1 Pure and Applied Analysis 1 Savoirs Actuels all top 5 Fields 107 Partial differential equations (35-XX) 46 Dynamical systems and ergodic theory (37-XX) 31 Operator theory (47-XX) 15 Global analysis, analysis on manifolds (58-XX) 15 Quantum theory (81-XX) 7 Functional analysis (46-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Functions of a complex variable (30-XX) 4 Fluid mechanics (76-XX) 4 Systems theory; control (93-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Differential geometry (53-XX) 3 Optics, electromagnetic theory (78-XX) 2 Special functions (33-XX) 2 Mechanics of deformable solids (74-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 97 Publications have been cited 2,973 times in 1,924 Documents Cited by ▼ Year ▼ Microlocal defect measures. Zbl 0770.35001 Gérard, Patrick 231 1991 Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Zbl 1067.58027 Burq, N.; Gérard, P.; Tzvetkov, N. 227 2004 High frequency approximation of solutions to critical nonlinear wave equations. Zbl 0919.35089 Bahouri, Hajer; Gérard, Patrick 225 1999 Homogenization limits and Wigner transforms. Zbl 0881.35099 Gérard, Patrick; Markowich, Peter A.; Mauser, Norbert J.; Poupaud, Frédéric 219 1997 Description of the lack of compactness for the Sobolev imbedding. Zbl 0907.46027 Gérard, P. 129 1998 A necessary and sufficient condition for the exact controllability of the wave equation. (Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes.) Zbl 0906.93008 Burq, Nicolas; Gérard, Patrick 123 1997 Ergodic properties of eigenfunctions for the Dirichlet problem. Zbl 0788.35103 Gérard, Patrick; Leichtnam, Eric 109 1993 Pseudo-differential operators and the Nash-Moser theorem. (Opérateurs pseudo-différentiels et théorème de Nash-Moser.) Zbl 0791.47044 Alinhac, Serge; Gérard, Patrick 105 1991 Pseudo-differential operators and the Nash–Moser theorem. Transl. from the French by Stephen S. Wilson. Zbl 1121.47033 Alinhac, Serge; Gérard, Patrick 96 2007 Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces. Zbl 1092.35099 Burq, N.; Gérard, P.; Tzvetkov, N. 85 2005 The cubic Szegő equation. (L’équation de Szegő cubique.) Zbl 1228.35225 Gérard, Patrick; Grellier, Sandrine 75 2010 Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds. Zbl 1131.35053 Burq, N.; Gérard, P.; Tzvetkov, N. 74 2007 Stabilization and control for the nonlinear Schrödinger equation on a compact surface. Zbl 1127.93015 Dehman, B.; Gérard, P.; Lebeau, G. 69 2006 An instability property of the nonlinear Schrödinger equation on \(S^d\). Zbl 1003.35113 Burq, N.; Gérard, P.; Tzvetkov, N. 64 2002 Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations. Zbl 1116.35109 Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay 59 2005 The Cauchy problem for the Gross–Pitaevskii equation. Zbl 1122.35133 Gérard, P. 57 2006 Sharp Sobolev inequalities. (Inégalités de Sobolev précisées.) Zbl 1066.46501 Gerard, Patrick; Meyer, Yves; Oru, Frédérique 52 1997 Mesures semi-classiques et ondes de Bloch. (Semiclassical measures and Bloch waves). Zbl 0739.35096 Gérard, P. 49 1991 Besov spaces and Strichartz estimates on the Heisenberg group. (Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg.) Zbl 0965.22010 Bahouri, Hajer; Gérard, Patrick; Xu, Chao-Jiang 49 2000 Effective integrable dynamics for a certain nonlinear wave equation. Zbl 1268.35013 Gérard, Patrick; Grellier, Sandrine 49 2012 On nonlinear Schrödinger equations in exterior domains. Zbl 1061.35126 Burq, N.; Gérard, P.; Tzvetkov, N. 47 2004 Oscillations of concentration effects in semilinear dispersive wave equations. Zbl 0868.35075 Gérard, Patrick 46 1996 Semi-classical measures and eigenvalue crossings. (Mesures semi-classiques et croisement de modes.) Zbl 0996.35004 Fermanian-Kammerer, Clotilde; Gérard, Patrick 42 2002 The cubic Szegő equation and Hankel operators. Zbl 1410.37001 Gérard, Patrick; Grellier, Sandrine 39 2017 An explicit formula for the cubic Szegő equation. Zbl 1318.37024 Gérard, Patrick; Grellier, Sandrine 34 2015 Invariant tori for the cubic Szegö equation. Zbl 1252.35026 Gérard, Patrick; Grellier, Sandrine 33 2012 The Gross-Pitaevskii equation in the energy space. Zbl 1166.35373 Gérard, Patrick 28 2008 A Landau-Zener formula for non-degenerated involutive codimension 3 crossings. Zbl 1049.81029 Fermanian Kammerer, Clotilde; Gérard, Patrick 28 2003 On the integrability of the Benjamin-Ono equation on the torus. Zbl 1471.35354 Gérard, Patrick; Kappeler, Thomas 27 2021 Two singular dynamics of the nonlinear Schrödinger equation on a plane domain. Zbl 1044.35084 Burq, N.; Gérard, P.; Tzvetkov, N. 26 2003 A two-soliton with transient turbulent regime for the cubic half-wave equation on the real line. Zbl 1397.35062 Gérard, Patrick; Lenzmann, Enno; Pocovnicu, Oana; Raphaël, Pierre 26 2018 Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation. Zbl 1232.35152 Gérard, Patrick; Zhang, Zhifei 25 2009 On the radius of analyticity of solutions to the cubic Szegő equation. Zbl 1332.35058 Gérard, Patrick; Guo, Yanqiu; Titi, Edriss S. 18 2015 On the cubic lowest Landau level equation. Zbl 1412.82034 Gérard, Patrick; Germain, Pierre; Thomann, Laurent 18 2019 Moyennisation et régularité deux-microlocale. (Second microlocal averaging and regularity). Zbl 0725.35003 Gérard, Patrick 17 1990 Averaging regularity results for PDEs under transversality assumptions. Zbl 0832.35020 Gérard, Patrick; Golse, François 17 1992 Global solutions for the nonlinear Schrödinger equation on three-dimensional compact manifolds. Zbl 1180.35475 Burq, N.; Gérard, P.; Tzvetkov, N. 17 2007 Remarks on the semiclassical analysis of the nonlinear Schrödinger equation. (Remarques sur l’analyse semi-classique de l’équation de Schrödinger non linéaire.) Zbl 0874.35111 Gérard, Patrick 17 1993 On the spectrum of the Lax operator of the Benjamin-Ono equation on the torus. Zbl 1452.37070 Gérard, Patrick; Kappeler, Thomas; Topalov, Petar 16 2020 Profile decomposition for the wave equation outside a convex obstacle. Zbl 0980.35088 Gallagher, Isabelle; Gérard, Patrick 15 2001 Diffraction of a wave at a corner. (Diffusion d’une onde par un coin.) Zbl 0779.35063 Gérard, Patrick; Lebeau, Gilles 13 1993 A Lax pair structure for the half-wave maps equation. Zbl 1393.37074 Gérard, Patrick; Lenzmann, Enno 12 2018 Nonlinear Schrödinger equation on four-dimensional compact manifolds. Zbl 1183.35251 Gérard, Patrick; Pierfelice, Vittoria 11 2010 The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold. Zbl 1362.35282 Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay 11 2003 Sharp well-posedness results of the Benjamin-Ono equation in \(H^s(\mathbb{T},\mathbb{R})\) and qualitative properties of its solutions. Zbl 1533.35061 Gérard, Patrick; Kappeler, Thomas; Topalov, Peter 11 2023 Recent results concerning two-dimensional incompressible perfect fluids (after J.-Y. Chemin and J.-M. Delort). (Résultats récents sur les fluides parfaits incompressibles bidimensionnels (d’après J.-Y. Chemin et J.-M. Delort).) Zbl 1154.76321 Gérard, Patrick 10 1992 Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem. Zbl 1106.35096 Gérard, Patrick 10 2006 Stabilization of wave equations on the torus with rough dampings. Zbl 1462.35070 Burq, Nicolas; Gérard, Patrick 10 2020 An explicit formula for the Benjamin-Ono equation. Zbl 1531.37066 Gérard, Patrick 10 2023 Wigner measure propagation and conical singularity for general initial data. Zbl 1288.35408 Fermanian-Kammerer, Clotilde; Gérard, Patrick; Lasser, Caroline 9 2013 Propagation de la régularité locale de solutions d’équations hyperboliques non linéaires. (Propagation of local smoothness for solutions of nonlinear hyperbolic equations). Zbl 0617.35079 Gerard, P.; Rauch, J. 9 1987 An inverse problem for self-adjoint positive Hankel operators. Zbl 1338.47024 Gérard, Patrick; Pushnitski, Alexander 8 2015 Multilinear estimates for the Laplace spectral projectors on compact manifolds. Zbl 1040.58011 Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay 8 2004 Unbounded Hankel operators and the flow of the cubic Szegő equation. Zbl 1525.47058 Gérard, Patrick; Pushnitski, Alexander 7 2023 On the Benjamin-Ono equation on \(\mathbb{T}\) and its periodic and quasiperiodic solutions. Zbl 1495.37060 Gérard, Patrick; Kappeler, Thomas; Topalov, Petar 7 2022 The cubic Szegő flow at low regularity. Zbl 1475.35434 Gérard, Patrick; Koch, Herbert 7 2017 On the analytic Birkhoff normal form of the Benjamin-Ono equation and applications. Zbl 1521.37085 Gérard, Patrick; Kappeler, Thomas; Topalov, Petar 7 2022 Inverse spectral problems for compact Hankel operators. Zbl 1304.47038 Gérard, Patrick; Grellier, Sandrine 6 2014 The cubic Szegö equation. (L’equation de Szegö cubique.) Zbl 1213.35397 Gérard, Patrick; Grellier, Sandrine 6 2010 A drift homogenization problem revisited. Zbl 1270.35058 Briane, Marc; Gérard, Patrick 6 2012 The Schrödinger equation on a compact manifold: Strichartz estimates and applications. Zbl 1043.58019 Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay 6 2001 Weighted model spaces and Schmidt subspaces of Hankel operators. Zbl 1448.47040 Gérard, Patrick; Pushnitski, Alexander 6 2020 Sensitivity phenomena for certain thin elastic shells with edges. Zbl 0989.74047 Gerard, Patrick; Sanchez-Palencia, Evariste 5 2000 Nonlinear Schrödinger equations on compact manifolds. Zbl 1076.35115 Gérard, P. 5 2005 The Cauchy problem for the nonlinear Schrödinger equation on compact manifolds. Zbl 1084.35086 Burq, N.; Gérard, P.; Tzvetkov, N. 5 2004 The Calogero-Moser derivative nonlinear Schrödinger equation. Zbl 07896921 Gérard, Patrick; Lenzmann, Enno 5 2024 Inverse spectral theory for a class of non-compact Hankel operators. Zbl 07036937 Gérard, Patrick; Pushnitski, Alexander 5 2019 On the growth of Sobolev norms for the cubic Szegő equation. Zbl 1355.35022 Gérard, Patrick; Grellier, Sandrine 4 2016 Compacité par compensation et régularité 2-microlocale. (Compensated compactness and 2-microlocal regularity). Zbl 0707.35032 Gérard, P. 3 1989 Concentration effects in critical nonlinear wave equation and scattering theory. Zbl 0926.35090 Bahouri, Hajer; Gérard, Patrick 3 1997 Solutions conormales analytiques d’équations hyperboliques non linéaires. (Conormal analytic solutions of nonlinear hyperbolic equations). Zbl 0639.35054 Gerard, Patrick 3 1988 Moyennes de solutions d’équations aux dérivées partielles. (Means of solutions of partial differential equations). Zbl 0657.35020 Gerard, P. 3 1987 The Schrödinger-Poisson system on the sphere. Zbl 1231.35229 Gérard, Patrick; Méhats, Florian 3 2011 Semiclassical measures and crossing of modes. (Mesures semi-classiques et croisement de modes.) Zbl 1055.81534 Fermanian Kammerer, Clotilde; Gerard, Patrick 3 2000 The zero dispersion limit for the Benjamin-Ono equation on the line. (Limite à faible dispersion pour l’équation de Benjamin-Ono sur la droite.) Zbl 07887262 Gérard, Patrick 3 2024 The cubic Szegő equation on the real line: explicit formula and well-posedness on the Hardy class. Zbl 07877943 Gérard, Patrick; Pushnitski, Alexander 3 2024 On a damped Szegö equation (with an appendix in collaboration with Christian Klein). Zbl 1448.35022 Gérard, Patrick; Grellier, Sandrine 3 2020 A nonlinear Fourier transform for the Benjamin-Ono equation on the torus and applications. Zbl 1479.35020 Gérard, Patrick 3 2020 A compactness result for generalized Radon transforms. Zbl 0864.44001 Gérard, Patrick; Golse, François; Wennberg, Bernt 2 1996 A microlocal version of concentration-compactness. Zbl 0868.35005 Gérard, Patrick 2 1996 Régularité de moyennes de solutions d’équations aux dérivées partielles. (Regularity of means of solutions of partial differential equations). Zbl 0639.35010 Gerard, Patrick 2 1987 A mean-field toy model for resonant transport. Zbl 1194.35462 Gerard, Patrick; Pallard, Christophe 2 2010 A survey of the Szegő equation. Zbl 1428.35067 Gérard, Patrick; Grellier, Sandrine 2 2019 Wave turbulence and complete integrability. Zbl 1442.35419 Gérard, Patrick 2 2019 A Landau-Zener formula for a generic crossing in codimension 2. (Une formule de Landau-Zener pour un croisement générique de codimension 2.) Zbl 1292.35252 Fermanian Kammerer, Clotilde; Gérard, Patrick 2 2002 The structure of Schmidt subspaces of Hankel operators: a short proof. Zbl 1514.47053 Gérard, Patrick; Pushnitski, Alexander 2 2021 Solutions globales du problème de Cauchy pour l’équation de Boltzmann [d’après R. J. Di Perna et P. L. Lions]. Zbl 0704.76041 Gérard, Patrick 1 1988 Regularization by averaging for solutions of partial differential equations. Zbl 0724.35115 Gérard, P. 1 1988 A Landau-Zener formula for two-scaled Wigner measures. Zbl 1145.81368 Fermanian Kammerer, Clotilde; Gerard, Patrick 1 2004 Generalized geometric optics for critical nonlinear waves. (Optique géométrique généralisée pour les ondes non linéaires critiques.) Zbl 1068.35522 Bahouri, Hajer; Gerard, Patrick 1 1997 An example of singular dynamics for the nonlinear Schrödinger equation on bounded domains. Zbl 1210.35225 Burg, N.; Gérard, P.; Tzvetkov, N. 1 2003 Generalized Strichartz estimates on the Heisenberg group. (Estimation de Strichartz généralisées sur le groupe de Heisenberg.) Zbl 1104.35303 Bahouri, Hajer; Gerard, Patrick; Xu, Chao-Jiang 1 1998 A Nekhoroshev theorem for some perturbations of the Benjamin-Ono equation with initial data close to finite gap tori. Zbl 07873282 Bambusi, Dario; Gérard, Patrick 1 2024 An introduction to the cubic Szegö equation. Zbl 1348.35232 Gérard, Patrick 1 2013 Two-scale Wigner measures and the Landau-Zener formulas. Zbl 1322.81059 Kammerer, C. Fermanian; Gérard, P. 1 2004 Inverse spectral problem for a pair of self-adjoint Hankel operators. Zbl 1449.35032 Gérard, Patrick; Grellier, Sandrine 1 2017 Generic colourful tori and inverse spectral transform for Hankel operators. Zbl 1409.35045 Gérard, Patrick; Grellier, Sandrine 1 2019 The Calogero-Moser derivative nonlinear Schrödinger equation. Zbl 07896921 Gérard, Patrick; Lenzmann, Enno 5 2024 The zero dispersion limit for the Benjamin-Ono equation on the line. (Limite à faible dispersion pour l’équation de Benjamin-Ono sur la droite.) Zbl 07887262 Gérard, Patrick 3 2024 The cubic Szegő equation on the real line: explicit formula and well-posedness on the Hardy class. Zbl 07877943 Gérard, Patrick; Pushnitski, Alexander 3 2024 A Nekhoroshev theorem for some perturbations of the Benjamin-Ono equation with initial data close to finite gap tori. Zbl 07873282 Bambusi, Dario; Gérard, Patrick 1 2024 Sharp well-posedness results of the Benjamin-Ono equation in \(H^s(\mathbb{T},\mathbb{R})\) and qualitative properties of its solutions. Zbl 1533.35061 Gérard, Patrick; Kappeler, Thomas; Topalov, Peter 11 2023 An explicit formula for the Benjamin-Ono equation. Zbl 1531.37066 Gérard, Patrick 10 2023 Unbounded Hankel operators and the flow of the cubic Szegő equation. Zbl 1525.47058 Gérard, Patrick; Pushnitski, Alexander 7 2023 On the Benjamin-Ono equation on \(\mathbb{T}\) and its periodic and quasiperiodic solutions. Zbl 1495.37060 Gérard, Patrick; Kappeler, Thomas; Topalov, Petar 7 2022 On the analytic Birkhoff normal form of the Benjamin-Ono equation and applications. Zbl 1521.37085 Gérard, Patrick; Kappeler, Thomas; Topalov, Petar 7 2022 On the integrability of the Benjamin-Ono equation on the torus. Zbl 1471.35354 Gérard, Patrick; Kappeler, Thomas 27 2021 The structure of Schmidt subspaces of Hankel operators: a short proof. Zbl 1514.47053 Gérard, Patrick; Pushnitski, Alexander 2 2021 On the spectrum of the Lax operator of the Benjamin-Ono equation on the torus. Zbl 1452.37070 Gérard, Patrick; Kappeler, Thomas; Topalov, Petar 16 2020 Stabilization of wave equations on the torus with rough dampings. Zbl 1462.35070 Burq, Nicolas; Gérard, Patrick 10 2020 Weighted model spaces and Schmidt subspaces of Hankel operators. Zbl 1448.47040 Gérard, Patrick; Pushnitski, Alexander 6 2020 On a damped Szegö equation (with an appendix in collaboration with Christian Klein). Zbl 1448.35022 Gérard, Patrick; Grellier, Sandrine 3 2020 A nonlinear Fourier transform for the Benjamin-Ono equation on the torus and applications. Zbl 1479.35020 Gérard, Patrick 3 2020 On the cubic lowest Landau level equation. Zbl 1412.82034 Gérard, Patrick; Germain, Pierre; Thomann, Laurent 18 2019 Inverse spectral theory for a class of non-compact Hankel operators. Zbl 07036937 Gérard, Patrick; Pushnitski, Alexander 5 2019 A survey of the Szegő equation. Zbl 1428.35067 Gérard, Patrick; Grellier, Sandrine 2 2019 Wave turbulence and complete integrability. Zbl 1442.35419 Gérard, Patrick 2 2019 Generic colourful tori and inverse spectral transform for Hankel operators. Zbl 1409.35045 Gérard, Patrick; Grellier, Sandrine 1 2019 A two-soliton with transient turbulent regime for the cubic half-wave equation on the real line. Zbl 1397.35062 Gérard, Patrick; Lenzmann, Enno; Pocovnicu, Oana; Raphaël, Pierre 26 2018 A Lax pair structure for the half-wave maps equation. Zbl 1393.37074 Gérard, Patrick; Lenzmann, Enno 12 2018 The cubic Szegő equation and Hankel operators. Zbl 1410.37001 Gérard, Patrick; Grellier, Sandrine 39 2017 The cubic Szegő flow at low regularity. Zbl 1475.35434 Gérard, Patrick; Koch, Herbert 7 2017 Inverse spectral problem for a pair of self-adjoint Hankel operators. Zbl 1449.35032 Gérard, Patrick; Grellier, Sandrine 1 2017 On the growth of Sobolev norms for the cubic Szegő equation. Zbl 1355.35022 Gérard, Patrick; Grellier, Sandrine 4 2016 An explicit formula for the cubic Szegő equation. Zbl 1318.37024 Gérard, Patrick; Grellier, Sandrine 34 2015 On the radius of analyticity of solutions to the cubic Szegő equation. Zbl 1332.35058 Gérard, Patrick; Guo, Yanqiu; Titi, Edriss S. 18 2015 An inverse problem for self-adjoint positive Hankel operators. Zbl 1338.47024 Gérard, Patrick; Pushnitski, Alexander 8 2015 Inverse spectral problems for compact Hankel operators. Zbl 1304.47038 Gérard, Patrick; Grellier, Sandrine 6 2014 Wigner measure propagation and conical singularity for general initial data. Zbl 1288.35408 Fermanian-Kammerer, Clotilde; Gérard, Patrick; Lasser, Caroline 9 2013 An introduction to the cubic Szegö equation. Zbl 1348.35232 Gérard, Patrick 1 2013 Effective integrable dynamics for a certain nonlinear wave equation. Zbl 1268.35013 Gérard, Patrick; Grellier, Sandrine 49 2012 Invariant tori for the cubic Szegö equation. Zbl 1252.35026 Gérard, Patrick; Grellier, Sandrine 33 2012 A drift homogenization problem revisited. Zbl 1270.35058 Briane, Marc; Gérard, Patrick 6 2012 The Schrödinger-Poisson system on the sphere. Zbl 1231.35229 Gérard, Patrick; Méhats, Florian 3 2011 The cubic Szegő equation. (L’équation de Szegő cubique.) Zbl 1228.35225 Gérard, Patrick; Grellier, Sandrine 75 2010 Nonlinear Schrödinger equation on four-dimensional compact manifolds. Zbl 1183.35251 Gérard, Patrick; Pierfelice, Vittoria 11 2010 The cubic Szegö equation. (L’equation de Szegö cubique.) Zbl 1213.35397 Gérard, Patrick; Grellier, Sandrine 6 2010 A mean-field toy model for resonant transport. Zbl 1194.35462 Gerard, Patrick; Pallard, Christophe 2 2010 Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation. Zbl 1232.35152 Gérard, Patrick; Zhang, Zhifei 25 2009 The Gross-Pitaevskii equation in the energy space. Zbl 1166.35373 Gérard, Patrick 28 2008 Pseudo-differential operators and the Nash–Moser theorem. Transl. from the French by Stephen S. Wilson. Zbl 1121.47033 Alinhac, Serge; Gérard, Patrick 96 2007 Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds. Zbl 1131.35053 Burq, N.; Gérard, P.; Tzvetkov, N. 74 2007 Global solutions for the nonlinear Schrödinger equation on three-dimensional compact manifolds. Zbl 1180.35475 Burq, N.; Gérard, P.; Tzvetkov, N. 17 2007 Stabilization and control for the nonlinear Schrödinger equation on a compact surface. Zbl 1127.93015 Dehman, B.; Gérard, P.; Lebeau, G. 69 2006 The Cauchy problem for the Gross–Pitaevskii equation. Zbl 1122.35133 Gérard, P. 57 2006 Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem. Zbl 1106.35096 Gérard, Patrick 10 2006 Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces. Zbl 1092.35099 Burq, N.; Gérard, P.; Tzvetkov, N. 85 2005 Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations. Zbl 1116.35109 Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay 59 2005 Nonlinear Schrödinger equations on compact manifolds. Zbl 1076.35115 Gérard, P. 5 2005 Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds. Zbl 1067.58027 Burq, N.; Gérard, P.; Tzvetkov, N. 227 2004 On nonlinear Schrödinger equations in exterior domains. Zbl 1061.35126 Burq, N.; Gérard, P.; Tzvetkov, N. 47 2004 Multilinear estimates for the Laplace spectral projectors on compact manifolds. Zbl 1040.58011 Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay 8 2004 The Cauchy problem for the nonlinear Schrödinger equation on compact manifolds. Zbl 1084.35086 Burq, N.; Gérard, P.; Tzvetkov, N. 5 2004 A Landau-Zener formula for two-scaled Wigner measures. Zbl 1145.81368 Fermanian Kammerer, Clotilde; Gerard, Patrick 1 2004 Two-scale Wigner measures and the Landau-Zener formulas. Zbl 1322.81059 Kammerer, C. Fermanian; Gérard, P. 1 2004 A Landau-Zener formula for non-degenerated involutive codimension 3 crossings. Zbl 1049.81029 Fermanian Kammerer, Clotilde; Gérard, Patrick 28 2003 Two singular dynamics of the nonlinear Schrödinger equation on a plane domain. Zbl 1044.35084 Burq, N.; Gérard, P.; Tzvetkov, N. 26 2003 The Cauchy problem for the nonlinear Schrödinger equation on a compact manifold. Zbl 1362.35282 Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay 11 2003 An example of singular dynamics for the nonlinear Schrödinger equation on bounded domains. Zbl 1210.35225 Burg, N.; Gérard, P.; Tzvetkov, N. 1 2003 An instability property of the nonlinear Schrödinger equation on \(S^d\). Zbl 1003.35113 Burq, N.; Gérard, P.; Tzvetkov, N. 64 2002 Semi-classical measures and eigenvalue crossings. (Mesures semi-classiques et croisement de modes.) Zbl 0996.35004 Fermanian-Kammerer, Clotilde; Gérard, Patrick 42 2002 A Landau-Zener formula for a generic crossing in codimension 2. (Une formule de Landau-Zener pour un croisement générique de codimension 2.) Zbl 1292.35252 Fermanian Kammerer, Clotilde; Gérard, Patrick 2 2002 Profile decomposition for the wave equation outside a convex obstacle. Zbl 0980.35088 Gallagher, Isabelle; Gérard, Patrick 15 2001 The Schrödinger equation on a compact manifold: Strichartz estimates and applications. Zbl 1043.58019 Burq, Nicolas; Gérard, Patrick; Tzvetkov, Nikolay 6 2001 Besov spaces and Strichartz estimates on the Heisenberg group. (Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg.) Zbl 0965.22010 Bahouri, Hajer; Gérard, Patrick; Xu, Chao-Jiang 49 2000 Sensitivity phenomena for certain thin elastic shells with edges. Zbl 0989.74047 Gerard, Patrick; Sanchez-Palencia, Evariste 5 2000 Semiclassical measures and crossing of modes. (Mesures semi-classiques et croisement de modes.) Zbl 1055.81534 Fermanian Kammerer, Clotilde; Gerard, Patrick 3 2000 High frequency approximation of solutions to critical nonlinear wave equations. Zbl 0919.35089 Bahouri, Hajer; Gérard, Patrick 225 1999 Description of the lack of compactness for the Sobolev imbedding. Zbl 0907.46027 Gérard, P. 129 1998 Generalized Strichartz estimates on the Heisenberg group. (Estimation de Strichartz généralisées sur le groupe de Heisenberg.) Zbl 1104.35303 Bahouri, Hajer; Gerard, Patrick; Xu, Chao-Jiang 1 1998 Homogenization limits and Wigner transforms. Zbl 0881.35099 Gérard, Patrick; Markowich, Peter A.; Mauser, Norbert J.; Poupaud, Frédéric 219 1997 A necessary and sufficient condition for the exact controllability of the wave equation. (Condition nécessaire et suffisante pour la contrôlabilité exacte des ondes.) Zbl 0906.93008 Burq, Nicolas; Gérard, Patrick 123 1997 Sharp Sobolev inequalities. (Inégalités de Sobolev précisées.) Zbl 1066.46501 Gerard, Patrick; Meyer, Yves; Oru, Frédérique 52 1997 Concentration effects in critical nonlinear wave equation and scattering theory. Zbl 0926.35090 Bahouri, Hajer; Gérard, Patrick 3 1997 Generalized geometric optics for critical nonlinear waves. (Optique géométrique généralisée pour les ondes non linéaires critiques.) Zbl 1068.35522 Bahouri, Hajer; Gerard, Patrick 1 1997 Oscillations of concentration effects in semilinear dispersive wave equations. Zbl 0868.35075 Gérard, Patrick 46 1996 A compactness result for generalized Radon transforms. Zbl 0864.44001 Gérard, Patrick; Golse, François; Wennberg, Bernt 2 1996 A microlocal version of concentration-compactness. Zbl 0868.35005 Gérard, Patrick 2 1996 Ergodic properties of eigenfunctions for the Dirichlet problem. Zbl 0788.35103 Gérard, Patrick; Leichtnam, Eric 109 1993 Remarks on the semiclassical analysis of the nonlinear Schrödinger equation. (Remarques sur l’analyse semi-classique de l’équation de Schrödinger non linéaire.) Zbl 0874.35111 Gérard, Patrick 17 1993 Diffraction of a wave at a corner. (Diffusion d’une onde par un coin.) Zbl 0779.35063 Gérard, Patrick; Lebeau, Gilles 13 1993 Averaging regularity results for PDEs under transversality assumptions. Zbl 0832.35020 Gérard, Patrick; Golse, François 17 1992 Recent results concerning two-dimensional incompressible perfect fluids (after J.-Y. Chemin and J.-M. Delort). (Résultats récents sur les fluides parfaits incompressibles bidimensionnels (d’après J.-Y. Chemin et J.-M. Delort).) Zbl 1154.76321 Gérard, Patrick 10 1992 Microlocal defect measures. Zbl 0770.35001 Gérard, Patrick 231 1991 Pseudo-differential operators and the Nash-Moser theorem. (Opérateurs pseudo-différentiels et théorème de Nash-Moser.) Zbl 0791.47044 Alinhac, Serge; Gérard, Patrick 105 1991 Mesures semi-classiques et ondes de Bloch. (Semiclassical measures and Bloch waves). Zbl 0739.35096 Gérard, P. 49 1991 Moyennisation et régularité deux-microlocale. (Second microlocal averaging and regularity). Zbl 0725.35003 Gérard, Patrick 17 1990 Compacité par compensation et régularité 2-microlocale. (Compensated compactness and 2-microlocal regularity). Zbl 0707.35032 Gérard, P. 3 1989 Solutions conormales analytiques d’équations hyperboliques non linéaires. (Conormal analytic solutions of nonlinear hyperbolic equations). Zbl 0639.35054 Gerard, Patrick 3 1988 Solutions globales du problème de Cauchy pour l’équation de Boltzmann [d’après R. J. Di Perna et P. L. Lions]. Zbl 0704.76041 Gérard, Patrick 1 1988 Regularization by averaging for solutions of partial differential equations. Zbl 0724.35115 Gérard, P. 1 1988 Propagation de la régularité locale de solutions d’équations hyperboliques non linéaires. (Propagation of local smoothness for solutions of nonlinear hyperbolic equations). Zbl 0617.35079 Gerard, P.; Rauch, J. 9 1987 Moyennes de solutions d’équations aux dérivées partielles. (Means of solutions of partial differential equations). Zbl 0657.35020 Gerard, P. 3 1987 Régularité de moyennes de solutions d’équations aux dérivées partielles. (Regularity of means of solutions of partial differential equations). Zbl 0639.35010 Gerard, Patrick 2 1987 all cited Publications top 5 cited Publications all top 5 Cited by 1,677 Authors 46 Gerard, Patrick 41 Tzvetkov, Nikolay 37 Burq, Nicolas 34 Cavalcanti, Marcelo Moreira 30 Fermanian-Kammerer, Clotilde 29 Carles, Rémi 26 Domingos Cavalcanti, Valéria Neves 24 Kenig, Carlos Eduardo 22 Duyckaerts, Thomas 20 Bahouri, Hajer 18 Bal, Guillaume 17 Gallagher, Isabelle 17 Jin, Shi 17 Visciglia, Nicola 16 Oh, Tadahiro 15 Markowich, Peter Alexander 15 Merle, Frank 15 Paul, Thierry 15 Ryzhik, Lenya 14 Antonić, Nenad 14 Gala, Sadek 14 Nakanishi, Kenji 14 Thomann, Laurent 14 Zuazua, Enrique 13 Macià, Fabricio 13 Panov, Evgeniy Yu. 12 Galkowski, Jeffrey 12 Laurent, Camille 12 Lawrie, Andrew G. W. 12 Léautaud, Matthieu 12 Miao, Changxing 11 Hani, Zaher 11 Israwi, Samer 11 Lebeau, Gilles 11 Mauser, Norbert Julius 11 Sun, Chenmin 11 Tataru, Daniel 11 Visan, Monica 10 Evnin, Oleg 10 Guo, Zihua 10 Ibrahim, Slim 10 Krieger, Joachim 10 Lasser, Caroline 10 Lazar, Martin 10 Masmoudi, Nader 10 Mitrovic, Darko 10 Perthame, Benoît 10 Ragusa, Maria Alessandra 10 Raphael, Pierre 10 Saut, Jean-Claude 10 Sogge, Christopher D. 10 Tacy, Melissa 10 Trélat, Emmanuel 9 Banica, Valeria 9 Grellier, Sandrine 9 Khorbatly, Bashar 9 Killip, Rowan 9 Pelinovsky, Dmitry Efimovich 9 Planchon, Fabrice 9 Schlag, Wilhelm 9 Secchi, Paolo 9 Sparber, Christof 9 Toth, John Andrew 8 Allaire, Grégoire 8 Aloui, Lassaad 8 Blair, Matthew D. 8 Erceg, Marko 8 Ervedoza, Sylvain 8 Gassot, Louise 8 Gonzalez Martinez, Victor Hugo 8 Gravejat, Philippe 8 Guardia, Marcel 8 Hassell, Andrew 8 Majdoub, Mohamed 8 Pausader, Benoît 8 Soler, Juan S. 8 Xu, Guixiang 8 Zelditch, Steven Morris 8 Zhu, Shihui 7 Alabau-Boussouira, Fatiha 7 Bao, Weizhu 7 Brzeźniak, Zdzisław 7 Christianson, Hans 7 Corrêa, Wellington José 7 Dehman, Belhassen 7 Dodson, Benjamin G. 7 Germain, Pierre 7 Jendrej, Jacek 7 Kwon, Soonsik 7 Lee, Sanghyuk 7 Lenzmann, Enno 7 Méhats, Florian 7 Morando, Alessandro 7 Panthee, Mahendra 7 Pierfelice, Vittoria 7 Pinaud, Olivier 7 Pocovnicu, Oana 7 Privat, Yannick 7 Pushnitski, Alexander B. 7 Ruzhansky, Michael V. ...and 1,577 more Authors all top 5 Cited in 292 Serials 99 Journal of Differential Equations 74 Communications in Mathematical Physics 70 Journal of Functional Analysis 70 Communications in Partial Differential Equations 52 Archive for Rational Mechanics and Analysis 50 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 43 Journal de Mathématiques Pures et Appliquées. Neuvième Série 36 Journal of Mathematical Analysis and Applications 34 Journal of Mathematical Physics 34 Comptes Rendus. Mathématique. Académie des Sciences, Paris 33 Transactions of the American Mathematical Society 32 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 32 SIAM Journal on Mathematical Analysis 27 Nonlinearity 27 Analysis & PDE 24 Mathematische Annalen 24 Discrete and Continuous Dynamical Systems 22 Journal of the European Mathematical Society (JEMS) 21 Duke Mathematical Journal 21 Communications on Pure and Applied Analysis 20 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 19 Communications on Pure and Applied Mathematics 19 Journal of Computational Physics 18 Proceedings of the American Mathematical Society 18 Séminaire Laurent Schwartz. EDP et Applications 17 Bulletin de la Société Mathématique de France 17 Inventiones Mathematicae 17 The Journal of Geometric Analysis 16 Advances in Mathematics 16 Journal of Hyperbolic Differential Equations 15 Annales de l’Institut Fourier 15 Pure and Applied Analysis 14 Mathematical Methods in the Applied Sciences 14 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 14 Revista Matemática Iberoamericana 14 Journal of Dynamics and Differential Equations 14 Communications in Contemporary Mathematics 13 ZAMP. Zeitschrift für angewandte Mathematik und Physik 13 Mathematische Zeitschrift 13 Physica D 13 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 11 Wave Motion 11 Asymptotic Analysis 11 Annales Henri Poincaré 11 Journal of Spectral Theory 10 Journal d’Analyse Mathématique 10 Journal of the American Mathematical Society 10 NoDEA. Nonlinear Differential Equations and Applications 10 Science China. Mathematics 9 Applicable Analysis 9 Annali di Matematica Pura ed Applicata. Serie Quarta 9 SIAM Journal on Control and Optimization 9 Calculus of Variations and Partial Differential Equations 9 Journal of Pseudo-Differential Operators and Applications 9 Annals of PDE 8 Mathematische Nachrichten 8 Geometric and Functional Analysis. GAFA 8 The Journal of Fourier Analysis and Applications 8 Journal of Evolution Equations 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 Numerische Mathematik 7 Journal of Scientific Computing 7 Journal of Mathematical Sciences (New York) 7 Stochastic and Partial Differential Equations. Analysis and Computations 7 Evolution Equations and Control Theory 7 Journal de l’École Polytechnique – Mathématiques 6 Journal of Statistical Physics 6 Transport Theory and Statistical Physics 6 American Journal of Mathematics 6 Proceedings of the London Mathematical Society. Third Series 6 Quarterly of Applied Mathematics 6 Forum Mathematicum 6 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 6 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 6 Acta Mathematica Sinica. English Series 6 Nonlinear Analysis. Real World Applications 6 Multiscale Modeling & Simulation 6 Journal of Physics A: Mathematical and Theoretical 6 Annales Henri Lebesgue 5 Applied Mathematics and Optimization 5 Indiana University Mathematics Journal 5 Journal of the London Mathematical Society. Second Series 5 Memoirs of the American Mathematical Society 5 SIAM Journal on Applied Mathematics 5 Bulletin of the American Mathematical Society. New Series 5 Journal of Nonlinear Science 5 Discrete and Continuous Dynamical Systems. Series B 5 Journal of the Institute of Mathematics of Jussieu 5 Acta Numerica 5 Oberwolfach Reports 5 Discrete and Continuous Dynamical Systems. Series S 4 Letters in Mathematical Physics 4 Journal of Optimization Theory and Applications 4 Chinese Annals of Mathematics. Series B 4 Acta Applicandae Mathematicae 4 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 4 Potential Analysis 4 Applied and Computational Harmonic Analysis 4 St. Petersburg Mathematical Journal 4 Foundations of Computational Mathematics ...and 192 more Serials all top 5 Cited in 53 Fields 1,597 Partial differential equations (35-XX) 263 Quantum theory (81-XX) 215 Global analysis, analysis on manifolds (58-XX) 215 Fluid mechanics (76-XX) 214 Dynamical systems and ergodic theory (37-XX) 139 Systems theory; control (93-XX) 128 Statistical mechanics, structure of matter (82-XX) 113 Operator theory (47-XX) 109 Harmonic analysis on Euclidean spaces (42-XX) 99 Functional analysis (46-XX) 90 Numerical analysis (65-XX) 73 Mechanics of deformable solids (74-XX) 65 Probability theory and stochastic processes (60-XX) 52 Calculus of variations and optimal control; optimization (49-XX) 52 Differential geometry (53-XX) 52 Optics, electromagnetic theory (78-XX) 35 Ordinary differential equations (34-XX) 32 Topological groups, Lie groups (22-XX) 29 Abstract harmonic analysis (43-XX) 24 Real functions (26-XX) 18 Relativity and gravitational theory (83-XX) 17 Number theory (11-XX) 16 Functions of a complex variable (30-XX) 12 Special functions (33-XX) 11 Measure and integration (28-XX) 11 Mechanics of particles and systems (70-XX) 11 Geophysics (86-XX) 10 Integral equations (45-XX) 9 General and overarching topics; collections (00-XX) 9 Integral transforms, operational calculus (44-XX) 9 Biology and other natural sciences (92-XX) 8 Potential theory (31-XX) 8 Approximations and expansions (41-XX) 7 Astronomy and astrophysics (85-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Information and communication theory, circuits (94-XX) 4 Combinatorics (05-XX) 4 Several complex variables and analytic spaces (32-XX) 4 General topology (54-XX) 3 Group theory and generalizations (20-XX) 3 Difference and functional equations (39-XX) 3 Operations research, mathematical programming (90-XX) 2 History and biography (01-XX) 2 Algebraic geometry (14-XX) 2 Nonassociative rings and algebras (17-XX) 2 Sequences, series, summability (40-XX) 2 Geometry (51-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistics (62-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Associative rings and algebras (16-XX) 1 Computer science (68-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.