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

TL;DR

This paper proves the existence of globally conservative weak solutions for a class of two-component nonlinear dispersive wave equations beyond wave breaking, using variable transformations and ODE theory.

Contribution

It introduces a new variable transformation and establishes global solutions for the system beyond wave breaking, extending previous understanding of such equations.

Findings

Existence of globally conservative weak solutions beyond wave breaking

Transformation of the system into a semi-linear form

Application of ODE theory for global existence

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.