※ 시간: 16:00 - 17:00

In the present talk, we discuss properties and the asymptotic stability of spherically symmetric stationary solutions to the compressible Navier-Stokes equations in the exterior domain of a unit ball. We study two types of boundary conditions, i.e., inflow and outflow conditions. For both problems, we derive several properties of stationary solutions, especially convergence rates toward far fields. By making use of these rates, we derive a-priori estimate of the perturbation from the stationary solution in the suitable Sobolev space. It shows the asymptotic stability of the stationary solution. In this derivation, the relative energy form plays an essential role. For the outflow problem, we do not have to assume any smallness assumptions on the initial data for the outflow problem if it belongs to the suitable weighted Sobolev space. This result is shown by using the representation formula of the density. We also discuss the asymptotic stability with the non-symmetric initial perturbation from the stationary solution.