American Institute of Mathematical Sciences

March  2015, 35(3): 871-889. doi: 10.3934/dcds.2015.35.871

On the Cauchy problem for a generalized Camassa-Holm equation

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

Received  March 2014 Revised  May 2014 Published  October 2014

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 $B_{2,\infty}^{3/2}$.
Citation: Defu Chen, Yongsheng Li, Wei Yan. On the Cauchy problem for a generalized Camassa-Holm equation. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 871-889. doi: 10.3934/dcds.2015.35.871
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