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The Cauchy problem for periodic semilinear PDE in space variables [after Bourgain]. (Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d’espace [d’après Bourgain].) (French) Zbl 0870.35096
Séminaire Bourbaki. Volume 1994/95. Exposés 790-804. Paris: Société Mathématique de France, Astérisque. 237, 163-187, Exp. No.796 (1996).
Let but de cet exposé est de donner un aperçu d’une série de travaux récents de Bourgain sur le problème de Cauchy pour un certain nombre d’équations d’évolution classiques lorsque la variable d’espace varie dans le tore T n . Ces équations sont des EDP semilinéaires dispersives pour des fonctions définies dans l’espace temps n × ou T n × (n est la dimension d’espace).
MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
35Q53KdV-like (Korteweg-de Vries) equations
35G25Initial value problems for nonlinear higher-order PDE
35B10Periodic solutions of PDE