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

Fuente: arXiv
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Main Authors: Zhou, Yonghui, Li, Xiaowan
Format: Preprint
Published: 2024
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author Zhou, Yonghui
Li, Xiaowan
author_facet Zhou, Yonghui
Li, Xiaowan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2409_18140
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking
Zhou, Yonghui
Li, Xiaowan
Analysis of PDEs
Mathematical Physics
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.
title Globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking
topic Analysis of PDEs
Mathematical Physics
url https://arxiv.org/abs/2409.18140