On the Hunter--Saxton system

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October 2009, 12(3): 647-656. doi: 10.3934/dcdsb.2009.12.647

On the Hunter--Saxton system

1.	Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

Received April 2009 Revised May 2009 Published July 2009

Abstract
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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, global existence in time., local well-posedness, blow-up phenomena.

Mathematics Subject Classification: Primary: 35B35, 35G25; Secondary: 35L6.

Citation: Marcus Wunsch. On the Hunter--Saxton system. Discrete & Continuous Dynamical Systems - B, 2009, 12 (3) : 647-656. doi: 10.3934/dcdsb.2009.12.647

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