3-D flow of a compressible viscous micropolar fluid with spherical symmetry: Large time behavior of the solution

Abstract

We consider the non-stationary 3-D flow of a compressible viscous heat-conducting micropolar fluid in the domain that is the subset of R3 bounded with two concentric spheres that present solid thermo-insulated walls. Under the assumption that the fluid is perfect and polytropic in the thermodynamical sense as well as that the initial density and temperature are strictly positive and that the initial data are sufficiently smooth spherically symmetric functions, the corresponding problem with homogeneous boundary data has a unique generalized solution for any time interval [0,T], T∈R+. In this work we analyze large time behavior of the solution and prove its stabilization.