Global conservative solutions to the Camassa--Holm equation for initial data with nonvanishing asymptotics

Katrin Grunert; Helge Holden; Xavier Raynaud

doi:10.3934/dcds.2012.32.4209

Article Contents

2012, Volume 32, Issue 12: 4209-4227. Doi: 10.3934/dcds.2012.32.4209 open access

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Global conservative solutions to the Camassa--Holm equation for initial data with nonvanishing asymptotics

1.
Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim
2.
Centre of Mathematics for Applications, University of Oslo, NO-0316 Oslo

Received: May 31, 2011

Revised: December 31, 2011

Published: November 2012

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Abstract

We show existence of global conservative solutions of the Cauchy problem for the Camassa--Holm equation $u_t-u_{txx}+\kappa u_x+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ with nonvanishing and distinct spatial asymptotics.

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Mathematics Subject Classification: Primary: 35Q53, 35B30; Secondary: 35B35, 35D30.

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