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Indexed by:期刊论文

Date of Publication:2016-11-01

Journal:MONATSHEFTE FUR MATHEMATIK

Included Journals:SCIE、Scopus

Volume:181

Issue:3

Page Number:715-744

ISSN No.: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.