Preprint 2008-012

Dissipative solutions for the Camassa–Holm equation

Helge Holden and Xavier Raynaud

Abstract: We show that the Camassa–Holm equation u_t−u_xxt+3uu_x−2u_xu_xx−uu_xxx=0 possesses a global continuous semigroup of weak dissipative solutions for initial data u|_t=0 in H¹. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. Stability in terms of H¹ and L^∞ norm is discussed.

Paper:: Available as PDF (762 Kbytes).
Author(s):: Helge Holden, holden (at) math ntnu no; Xavier Raynaud, raynaud (at) math ntnu no
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Submitted by:: raynaud (at) math ntnu no; 2008-03-26.

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Last modified: 2008-03-28 16:14 UTC