Translator Disclaimer
March/April 2009 Local well-posedness of nonlocal Burgers equations
Sylvie Benzoni-Gavage
Differential Integral Equations 22(3/4): 303-320 (March/April 2009).

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.

Citation

Download Citation

Sylvie Benzoni-Gavage. "Local well-posedness of nonlocal Burgers equations." Differential Integral Equations 22 (3/4) 303 - 320, March/April 2009.

Information

Published: March/April 2009
First available in Project Euclid: 20 December 2012

zbMATH: 1240.35446
MathSciNet: MR2492823

Subjects:
Primary: 34K07, 35L60

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
18 PAGES


SHARE
Vol.22 • No. 3/4 • March/April 2009
Back to Top