Gain of regularity for a Korteweg - de Vries - Kawahara type equation

Abstract

We study the existence of local and global solutions, and the gain of regularity for the initial value problem associated to the Korteweg - de Vries - Kawahara (KdVK) equation perturbed by a dispersive term which appears in several fluids dynamics problems. The study of gain of regularity is motivated by the results obtained by Craig, Kappeler and Strauss [8].

Keywords

• Evolution equations
• weighted Sobolev space.