Differential and Integral Equations

Local well-posedness of nonlocal Burgers equations

Sylvie Benzoni-Gavage

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K07: Theoretical approximation of solutions 35L60: Nonlinear first-order hyperbolic equations


Benzoni-Gavage, Sylvie. Local well-posedness of nonlocal Burgers equations. Differential Integral Equations 22 (2009), no. 3/4, 303--320. https://projecteuclid.org/euclid.die/1356019776

Export citation