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On the global existence of dissipative solutions for the modified coupled Camassa-Holm system. (English) Zbl 06464797
Summary: This paper investigates the dynamic behavior of the modified coupled two-component Camassa-Holm dynamic system arisen from shallow water waves moving. By using a skillfully defined characteristic and a set of newly introduced variables, the original system is converted into a Lagrangian semilinear one in which the associated energy is introduced as an additional variable so as to obtain a well-posed initial-value problem, facilitating the study on the behavior of wave breaking. It is established that the solutions of the system continue as global dissipative solutions after wave breaking, which presents an interesting and useful result for better understanding the inevitable phenomenon before and after wave breaking.

MSC:
76 Fluid mechanics
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