Thomas Alazard Chargé de recherche au CNRS Département de Mathématiques et Applications Ecole Normale Supérieure, 45 rue d'Ulm, Paris F-75005 email: Thomas.Alazard at ens.fr Tel.: +33 (0)1 44 32 20 76 CV

Récent

Nonlinéarité et dispersion dans les équations des vagues et de Schrödinger, Mémoire d'habilitation (soutenue le 7 décembre 2011). On the Cauchy problem for water gravity waves (with Nicolas Burq and Claude Zuily), preprint, 110 pages, first version. The water-waves equations: from Zakharov to Euler (with Nicolas Burq and Claude Zuily), preprint, 19 pages.

Water waves

Paralinearization of the Dirichlet to Neumann operator, and regularity of diamond waves (with Guy Métivier), Communications in Partial Differential Equations, 34 (2009), 1632-1704. On the water waves equations with surface tension (with Nicolas Burq and Claude Zuily), Duke Mathematical Journal, 158 Number 3 (2011), 413-499. Strichartz estimates for water waves (with Nicolas Burq and Claude Zuily), Annales scientifiques de l'ENS, 44 (2011), 855-903. Les travaux de Iooss et Plotnikov sur les vagues tri-dimensionnelles, publié dans la Gazette de la SMF, octobre 2010, 20 pages.

WKB analysis of the nonlinear Schrödinger equations

Semi-classical limit of Schrödinger-Poisson equations in space dimension n≥3 (with Rémi Carles), Journal of Differential Equations 233 (2007), no. 1, 241-275. Loss of regularity for super-critical nonlinear Schrödinger equations (with Rémi Carles), Mathematische Annalen 343 (2009), 397-420. Super critical geometric optics for nonlinear Schrödinger equations (with Rémi Carles), Archive for Rational Mechanics and Analysis 194 (2009), 315-347. WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity (with Rémi Carles), Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 26 (2009), 959-977.

Low Mach number limit

Incompressible limit of the nonisentropic Euler equations with the solid wall boundary conditions, Advances in Differential Equations 10 (2005), no. 1, 19-44. Low Mach number limit of the full Navier-Stokes equations, Archive for Rational Mechanics and Analysis 180 (2006), no. 1, 1-73. Low Mach number flows and combustion, SIAM Journal on Mathematical Analysis 38 (2006), no. 4, 1186-1213. A minicourse on the low Mach number limit, Discrete and Continuous Dynamical Systems Series S. 3 (2008), 365-404.

Miscellaneous

Alentours de la limite incompressible, Séminaire Équations aux Dérivées Partielles. XEDP 2004-2005. Some recent results in asymptotic fluid mechanics, Analysis and Simulation of Fluid Dynamics, Adv. Math. Fluid Mech., Birkhäuser, Basel, 2006. Dynamique des gaz à faible nombre de Mach, Thèse de l'Université Bordeaux I, sous la direction de Guy Métivier. Limite semi-classique des équations de Schrödinger-Poisson (with Rémi Carles), Journées Équations aux Dérivées Partielles, Evian 2006. On the Cauchy problem and the Kato smoothing effect for water waves (with Nicolas Burq and Claude Zuily), RIMS Kokyuroku Bessatsu. Low regularity theory for the water-waves problem: canals and swimming pools (with Nicolas Burq and Claude Zuily), Journées Équations aux Dérivées Partielles, Biarritz 2011.