一维黏性Camassa-Holm方程描述的液体-固体的相互作用

Large time behavior for a simplified 1d viscous Camassa-Holm equation model of fluid-solid interaction

讨论一维液体-固体相互作用的模型。利用Banach不动点原理和算子半群理论得到液体-固体相互作用的系统的解是整体存在惟一的。利用能量估计得到系统解的整体存在性,以及在质点固体两侧液体对它的压力渐近消失。

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.