Asymptotic Behavior of Spherically Symmetric Solutions to the Compressible Navier–Stokes Equation Towards Stationary Waves
摘要
The present paper studies an asymptotic behavior of a spherically symmetric solution on the exterior domain of an unit ball for the compressible Navier–Stokes equation, describing a motion of viscous barotropic gas. Especially we study outflow problem, that is, the fluid blows out through boundary. Precisely we show an asymptotic stability of a spherically symmetric stationary solutions provided that an initial disturbance of the stationary solution is sufficiently small in the Sobolev space.