3-D flow of a compressible viscous micropolar fluid with spherical symmetry: a global existence theorem

We consider the nonstationary 3-D flow of a compressible viscous heat-conducting micropolar fluid in the domain to be the subset of R 3 bounded with two concentric spheres that present the solid thermo-insulated walls. In the thermodynamical sense the fluid is perfect and polytropic. We assume that the initial density and temperature are bounded from below with a positive constant and that the initial data are sufficiently smooth spherically symmetric functions. The starting problem is transformed into the Lagrangian description on the spatial domain ] 0 , 1 [ . In this work we prove that our problem has a generalized solution for any time interval [ 0 , T ] , T ∈ R + . The proof is based on the local existence theorem and the extension principle.