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Indexed by:期刊论文

Date of Publication:2018-08-01

Journal:DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Included Journals:SCIE

Volume:38

Issue:8

Page Number:4163-4187

ISSN No.:1078-0947

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

Abstract: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.