Differential and Integral Equations

Local well-posedness of nonlocal Burgers equations

Sylvie Benzoni-Gavage

Abstract

This paper is concerned with nonlocal generalizations of the inviscid Burgers equation arising as amplitude equations for weakly nonlinear surface waves. Under homogeneity and stability assumptions on the involved kernel it is shown that the Cauchy problem is locally well posed in $H^2(\mathbb R)$, and a blow-up criterion is derived. The proof is based on a priori estimates without loss of derivatives, and on a regularization of both the equation and the initial data.

Article information

Source
Differential Integral Equations Volume 22, Number 3/4 (2009), 303-320.

Dates
First available in Project Euclid: 20 December 2012