Some properties of a generalized solution for 3-D flow of a compressible viscous micropolar fluid model with spherical symmetry

Abstract

We consider the nonstationary 3-D flow of a compressible viscous and heat-conducting micropolar fluid bounded with two concentric spheres that present solid thermoinsulated walls. We assume that the fluid is perfect and polytropic in the thermodynamical sense, as well as that the initial density and temperature are strictly positive.We take sufficiently smooth spherically symmetric initial functions and analyze the corresponding problem with homogeneous boundary data. In this work we give the overview of the current progress in mathematical analysis of the described problem with particular emphasis on the existence theorems and the large time behavior of the solution.