EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR 3D VISCOUS CAMASSA-HOLM EQUATIONS WITH THE DAMPING TERM IN THE WHOLE SPACE

DOI: 10.18173/2354-1059.2023-0018

Abstract

We consider the 3D viscous Camassa-Holm equations with damping term in the whole space. We first prove the existence, uniqueness of global weak solutions to the equations. Then, the Sobolev regularity of the solutions is studied.