# American Institute of Mathematical Sciences

October  2016, 36(10): 5493-5508. doi: 10.3934/dcds.2016042

## Well-posedness and blow-up phenomena for a generalized Camassa-Holm equation

 1 Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China 2 Department of Mathematics, Sun Yat-sen University, 510275 Guangzhou

Received  November 2015 Revised  December 2015 Published  July 2016

We first establish the local existence and uniqueness of strong solutions for the Cauchy problem of a generalized Camassa-Holm equation in nonhomogeneous Besov spaces by using the Littlewood-Paley theory. Then, we prove that the solution depends continuously on the initial data in the corresponding Besov space. Finally, we derive a blow-up criterion and present a blow-up result and a blow-up rate of the blow-up solutions to the equation.
Citation: Jinlu Li, Zhaoyang Yin. Well-posedness and blow-up phenomena for a generalized Camassa-Holm equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5493-5508. doi: 10.3934/dcds.2016042
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