Dispersive perturbations of Burgers and hyperbolic equations I : local theory

Abstract

The aim of this paper is to show how a weakly dispersive perturbation of the inviscid Burgers equation improve (enlarge) the space of resolution of the local Cauchy problem. More generally we will review several problems arising from weak dispersive perturbations of nonlinear hyperbolic equations or systems.

33 pages, new remarks added and some typos corrected

References in corpus (4)

• Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations
• A para-differential renormalization technique for nonlinear dispersive equations
• Singularity Formation in a Surface Wave Model
• Nonlinear wave interactions for the Benjamin-Ono equation