Asymptotic behavior toward radially symmetric stationary solutions of the compressible Navier-Stokes equation (Nonlinear and Random Waves)

Abstract

This research is a joint work with Professor Shinya Nishibata, Souhei Sugizaki of Tokyo institute of technology and Akitaka Matsumura of Osaka university. The present talk is concerned with the existence and asymptotic behaviors of radially symmetric stationary solutions for the compressible Navier-Stokes equation, describing the motion of viscous barotropic gas without external forces, where boundary and far field data are prescribed on the exterior domain in ℝ[n], n ≥ 3. We clear that for both inflow and outflow problems, there exist non trivial stationary solution, and for outflow problem we show that the stationary wave are asymptotic stable in a suitably small neighborhood of the initial data. Furthermore, detailed decay rate of the stationary solutions are derived.