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Global dissipative solutions for the two-component Camassa-Holm shallow water system. (English) Zbl 1315.35125
Summary: This article presents a continuous semigroup of globally defined weak dissipative solutions for the two-component Camassa-Holm system. Such solutions are established by using a new approach based on characteristics a set of new variables overcoming the difficulties inherent in multi-component systems.
MSC:
35L65 Hyperbolic conservation laws
35L51 Second-order hyperbolic systems
35Q35 PDEs in connection with fluid mechanics
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