Journal of Mathematical Fluid Mechanics

, Volume 14, Issue 3, pp 455–469

Global Existence for the Generalized Two-Component Hunter–Saxton System

Article

DOI: 10.1007/s00021-011-0075-9

Cite this article as:
Wu, H. & Wunsch, M. J. Math. Fluid Mech. (2012) 14: 455. doi:10.1007/s00021-011-0075-9

Abstract

We study the global existence of solutions to a two-component generalized Hunter–Saxton system in the periodic setting. We first prove a persistence result for the solutions. Then for some particular choices of the parameters (α, κ), we show the precise blow-up scenarios and the existence of global solutions to the generalized Hunter–Saxton system under proper assumptions on the initial data. This significantly improves recent results.

Mathematics Subject Classification (2010)

Primary 35B10Secondary 35Q35

Keywords

Generalized Hunter–Saxton systemGlobal existenceBlow-up scenario

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  2. 2.Department of MathematicsSwiss Federal Institute of Technology ZurichZurichSwitzerland