Global weak solutions for a three-component Camassa-Holm system with N-peakon solutions

TL;DR

This paper establishes the existence of global weak solutions for a three-component Camassa-Holm system, using approximation, regularization, and structural analysis, contributing to the mathematical understanding of complex nonlinear wave equations.

Contribution

It proves the existence of global weak solutions for a three-component Camassa-Holm system, a novel result in the study of multi-component nonlinear wave equations.

Findings

Existence of global weak solutions is proven.

Methodology involves approximation and regularization techniques.

Structural properties of the system are exploited.

Abstract

In this paper we mainly investigate the Cauchy problem of a three-component Camassa-Holm system. By using the method of approximation of smooth solutions, a regularization technique and the special structure of the system, we prove the existence of global weak solutions to the system.