Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation

2015/05/01 by Tu, Xi, Yin, Zhaoyang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.00086

Abstract

In this paper we mainly study the Cauchy problem for a generalized Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and transport equations theory, we establish the local well-posedness for the Cauchy problem of the equation in Besov spaces. Then we give a simply blow-up criterion for the Cauchy problem of the equation. we present a blow-up result and the exact blow-up rate of strong solutions to the equation by making use of the conservation law and the obtained blow-up criterion.Finally, we verify that the system possesses peakon solutions.

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