Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

On the Hunter--Saxton system

Pages: 647 - 656, Volume 12, Issue 3, October 2009      doi:10.3934/dcdsb.2009.12.647

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Marcus Wunsch - Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan (email)

Abstract: We show local existence of solutions to a two-component Hunter--Saxton system. Moreover, we prove that the slopes of solutions can become unbounded. Finally, if initial data satisfy appropriate smallness conditions, the associated flow is global.

Keywords:  Two-component Hunter--Saxton system, local well-posedness, blow-up phenomena, global existence in time.
Mathematics Subject Classification:  Primary: 35B35, 35G25; Secondary: 35L67.

Received: April 2009;      Revised: May 2009;      Available Online: July 2009.