Dissipative solutions for the Camassa-Holm equation

Helge Holden, Xavier Raynaud

Type: Article

Publication Date: 2009-01-01

Citations: 152

DOI: https://doi.org/10.3934/dcds.2009.24.1047

Abstract

We show that the Camassa--Holm equation$u_t-$uxxt+3uux-$2u_xuxx-uuxxx=0possesses a global continuous semigroup of weakdissipative solutions for initial data $u|_{t=0}$in $H^1$. The result is obtained by introducing acoordinate transformation into Lagrangiancoordinates. Stability in terms of $H^1$ and $L^\infty$ norm is discussed.

Locations

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