# American Institute of Mathematical Sciences

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March  2015, 35(3): 1327-1358. doi: 10.3934/dcds.2015.35.1327

## On the initial value problem for higher dimensional Camassa-Holm equations

 1 College of Information Science and Technology, Jinan University, Guangzhou, 510632, China 2 Department of Mathematics, Zhongshan University, Guangzhou, 510275

Received  April 2014 Revised  July 2014 Published  October 2014

This paper is concerned with the the initial value problem for higher dimensional Camassa-Holm equations. Firstly, the local well-posedness for this equations in both supercritical and critical Besov spaces are established. Then two blow-up criterions of strong solutions to the equations are derived. Finally, the analyticity of its solutions is proved in both variables, globally in space and locally in time.
Citation: Kai Yan, Zhaoyang Yin. On the initial value problem for higher dimensional Camassa-Holm equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 1327-1358. doi: 10.3934/dcds.2015.35.1327
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