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Dissipative solutions for the Camassa-Holm equation

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  • We show that the Camassa--Holm equation $u_t-$uxxt+3uux-$2u_xuxx-uuxxx=0 possesses a global continuous semigroup of weak dissipative solutions for initial data $u|_{t=0}$ in $H^1$. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. Stability in terms of $H^1$ and $L^\infty$ norm is discussed.
    Mathematics Subject Classification: Primary: 65M06, 65M12; Secondary: 35B10, 35Q53.

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