Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation
Analysis of PDEs
2015-07-21 v2
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.
Keywords
Cite
@article{arxiv.1505.00086,
title = {Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation},
author = {Xi Tu and Zhaoyang Yin},
journal= {arXiv preprint arXiv:1505.00086},
year = {2015}
}