On the Hunter--Saxton system

Marcus Wunsch

doi:10.3934/dcdsb.2009.12.647

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2009, Volume 12, Issue 3: 647-656. Doi: 10.3934/dcdsb.2009.12.647

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On the Hunter--Saxton system

Marcus Wunsch^1,

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

Received: April 2009

Revised: May 2009

Published: May 2009

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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.

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Mathematics Subject Classification: Primary: 35B35, 35G25; Secondary: 35L67.

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