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.

Abstract. An initial-boundary value problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid is considered. It is assumed that the fluid is thermodynamically perfect and polytropic. A problem has a unique strong solution on ]0, 1[×]0, T [, for each T > 0. Using this result we obtain a priori estimates for the solution independent of T .

We consider 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 solid thermoinsulated walls. In thermodynamical sense fluid is perfect and polytropic. Assuming that the initial density and temperature are strictly positive we will prove that for smooth enough spherically symmetric initial data there exists a spherically symmetric generalized solution locally in time.

No abstract

Abstract. An initial-boundary value problem for 1-D flow of a compressible viscous heat-conducting micropolar fluid is considered; the fluid is assumed thermodynamically perfect and polytropic. By transforming the original problem into homogeneous one we prove a global-in-time existence theorem. The proof is based on a local existence theorem, obtained in the previous research paper [5].Mathematics subject classification (2000): 35K55, 35Q40, 76N10, 46E35.