Global existence for the generalized two-component Hunter-Saxton system

2010/09/09 by Hao Wu, Marcus Wunsch
Mathematics · #math.AP #msc:35B10 #msc:35B65 #msc:35Q35 #msc:35Q85

paper · pdf · doi:10.1007/s00021-011-0075-9

published as J. Math. Fluid Mech. 14 (2012), 455-469 · 22 pages; submitted in modified form on August 7, 2010

arxiv created 2010/09/09 · arxiv updated 2012/10/24

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 of the solutions. Then for some particular choices of 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 obtained in [M. Wunsch, DCDS Ser. B 12 (2009), 647-656] and [M. Wunsch, SIAM J. Math. Anal. 42 (2010), 1286-1304].

Cited by

• An integrable semi-discretization of the two-component Hunter-Saxton equation