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Global weak solutions for a shallow water equation. (English) Zbl 0930.35133
Using the method of compensated compactness, the authors prove the existence of a global weak solution to the initial value problem for the Camassa-Holm equation $u_t- u_{xxt}+ 3uu_x= 2u_x u_{xx}+ uu_{xxx}$, $t>0$, $x\in\bbfR$, $u(0, x)= u_0(x)\in H^1(\bbfR)$. This problem describes a unidirectional propagation of water waves on a free surface, and is capable of treating the interaction of peaked solutions (solitons with cusp singularities).
Reviewer: O.Titow (Berlin)

35Q35PDEs in connection with fluid mechanics
76B25Solitary waves (inviscid fluids)
35Q51Soliton-like equations
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