Differential and Integral Equations
- Differential Integral Equations
- Volume 22, Number 3/4 (2009), 303-320.
Local well-posedness of nonlocal Burgers equations
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.
Differential Integral Equations Volume 22, Number 3/4 (2009), 303-320.
First available in Project Euclid: 20 December 2012
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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.