Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2016-11-01

Journal: MONATSHEFTE FUR MATHEMATIK

Included Journals: Scopus、SCIE

Volume: 181

Issue: 3

Page Number: 715-744

ISSN: 0026-9255

Key Words: Generalized mu-Hunter-Saxton equation; Weakly dissipative; Wave breaking; Holder continuity; Global existence

Abstract: In this paper, we study the Cauchy problem of a weakly dissipative generalized -Hunter-Saxton equation in the periodic setting. We first establish the local well-posedness for the generalized equation in Sobolev spaces , . Then we obtain a wave-breaking criterion for strong solutions and some results of wave-breaking solutions with certain initial profiles. We also determine the exact blow-up rate of strong solutions. Moreover, we show that the solution map for the generalized equation is Holder continuous in , , equipped with the -topology for . Finally, we give the global existence results for strong solutions and weak solutions.