On the Cauchy problem for a generalized Camassa-Holm equation

Defu Chen; Yongsheng Li; Wei Yan

doi:10.3934/dcds.2015.35.871

Article Contents

2015, Volume 35, Issue 3: 871-889. Doi: 10.3934/dcds.2015.35.871

This issue Previous Article Non ultracontractive heat kernel bounds by Lyapunov conditions Next Article Blow up of solutions of semilinear heat equations in non radial domains of $\mathbb{R}^2$

On the Cauchy problem for a generalized Camassa-Holm equation

1.
Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640
2.
College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007

Received: February 28, 2014

Revised: April 30, 2014

Published: February 2015

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Abstract

In this paper, we consider the Cauchy problem for a generalized Camassa-Holm equation. We establish the local well-posedness in the Besov space $B_{2,1}^{3/2}$ and also prove that the local well-posedness fails in the Besov space $B_{2,\infty}^{3/2}$.

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Mathematics Subject Classification: Primary: 35Q53; Secondary: 35G25, 35A01.

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