engleski

3-D flow of a compressible viscous micropolar fluid with cylindrical symmetry: a local existence theorem

In this work we consider the nonstationary 3D flow of a compressible viscous and heatconducting micropolar fluid, which is in the thermodynamical sense perfect and polytropic. The fluid domain is the subset of R3 bounded with two coaxial cylinders that present solid thermoinsulated walls. We assume that the initial mass density, temperature, as well as the velocity and microrotation vectors are radially dependent only and analyze the corresponding initial-boundary value problem. With the additional assumptionthat the initial mass density and temperature are strictly positive we prove that for smooth enough initial data there exists a cylindrically symmetric generalized solution locally in time. The proof is based on the Faedo-Galerkin method.

cylindricall symmetry ; micropolar fluid ; local existence

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