Global weak solutions for a two-component Camassa–Holm system with an arbitrary smooth function

Abstract

In the paper, by the approximation of smooth solutions and a regularization technique, we show the existence and uniqueness of global weak solutions for a two-component Camassa–Holm system with an arbitrary smooth function provided the initial data satisfy some certain sign condition.

Keywords:

• A two-component Camassa–Holm system
• the approximation of smooth solutions
• a regularization technique
• global weak solutions

AMS Subject Classifications:

• 35G25
• 35L05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NNSFC [number 11671407]; FDCT [number 098/2013/A3]; Guangdong Special Support Program [number 8-2015]; the key project of NSF of Guangdong province [number 2016A030311004].