Sur l’existence et la stabilité de solutions du problème de Cauchy dans certains espaces fonctionnels

Abstract

The main objective of this thesis is to study the well-posedness and temporal regularity in Gevrey spaces and anisotropic Gevrey spaces for some partial differential equations. This thesis is divided into two parts: First one is to study the local and global well-posedness for the Kawahara equation and the m-Korteweg-de Vries system with the initial data in analytical Gevrey spaces. In addition, the Gevrey regularity of the solutions in variable time is provided. The second part consists in studying the local well-posedness and the time regularity for the Kadomtsev-Petviashvili I equation and the global well-posedness for the Kadomtsev Petviashvili II equation with initial data in anisotropic Gevrey space