Dispersive perturbations of Burgers and hyperbolic equations I : local theory

TL;DR

This paper investigates how weak dispersive perturbations enhance the local solvability of the inviscid Burgers equation and related hyperbolic systems, broadening the scope of initial data for which solutions exist.

Contribution

It introduces a framework for understanding the impact of weak dispersive effects on hyperbolic equations, expanding the local well-posedness theory.

Findings

Weak dispersive perturbations enlarge the resolution space for Burgers equation

The approach applies to a class of nonlinear hyperbolic systems

Enhanced local existence results for perturbed hyperbolic equations

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.