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arXiv · 2409.18140

Globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking

Yonghui Zhou·Xiaowan Li
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Abstract

In this paper, we prove that the existence of globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking. We first introduce a new set of independent and dependent variables in connection with smooth solutions, and transform the system into an equivalent semi-linear system. We then establish the global existence of solutions for the semi-linear system via the standard theory of ordinary differential equations. Finally, by the inverse transformation method, we prove the existence of the globally conservative weak solution for the original system.

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Yonghui Zhou, Xiaowan Li. 2024-09-15. Globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking. https://arxiv.org/abs/2409.18140

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