# Long-Time Behavior of a Point Mass in a One-Dimensional Viscous Compressible Fluid

## Speaker

Kai Koike, Keio University

## Time

2019.08.02 10:00-11:00

## Venue

Room 306, No. 5, Science Building

## Abstract

We study the long-time behavior of a point mass in a 1D viscous compressible fluid. By using the technique of pointwise estimates of Green’s function, we prove pointwise estimates of the solution to the system of the fluid and the point mass. As a corollary, we show that the velocity $V(t)$ of the point mass decays with the power law $t^{-3/2}$, whereas the $L^{\infty}$-norm of the fluid variables decay as $t^{-1/2}$. The nonlinearity and the compressibility play essential roles in this phenomenon.