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论文类型：期刊论文

发表时间：2018-08-01

发表刊物：DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

收录刊物：SCIE

卷号：38

期号：8

页面范围：4163-4187

ISSN号：1078-0947

关键字：Higher-order mu-Camassa-Holm equation; global existence; weak solutions; non-uniformly continuous; peakon solutions

摘要：In this paper, we study the Cauchy problem of a higher-order mu-Camassa-Holm equation. We first establish the Green's function of (mu - (partial derivative(2)(x)+partial derivative(4)(x))(-1) and local well-posedness for the equation in Sobolev spaces H-s(S), s > 7/2. Then we provide the global existence results for strong solutions and weak solutions. Moreover, we show that the solution map is non-uniformly continuous in H-s(S), s >= 4. Finally, we prove that the equation admits single peakon solutions which have continuous second derivatives and jump discontinuities in the third derivatives.