2024/09/15 by Yonghui Zhou, Wenbin Li, Zhou, Yonghui +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2409.18140
openalex publication_date 2024/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.