Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-08-01

Journal: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Included Journals: SCIE

Volume: 38

Issue: 8

Page Number: 4163-4187

ISSN: 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.