Global dissipative solutions for the two-component Camassa-Holm shallow water system

Abstract

This article presents a continuous semigroup of globally defined weak dissipative solutions for the two-component Camassa-Holm system. Such solutions are established by using a new approach based on characteristics a set of new variables overcoming the difficulties inherent in multi-component systems.

Keywords

• Two-component Camassa-Holm system
• global solutions
• dissipative solutions