关键词: 一维黏性Camassa-Holm方程;液体-固体相互作用;Banach不动点原理;能量估计

Abstract:

A simple model in one space dimension for the interaction between a fluid and a solid represented by a point mass is considered. By using the semi-group theorem and Banach fixed-point theorem,  the existence and uniqueness of the solution to the system is proved. Furthermore,  the asymptotic behavior of solutions for integrable data using energy estimates is described. That asymptotically the difference of pressure to both sides of the point mass vanishes is also proved.

Key words: one-dimension viscous Camassa-Holm equation; fluid-Solid Interaction; Banach fixed-point theorem; energy estimate