The existence of a global solution for one dimensional compressible viscous micropolar fluid with non-homogeneous boundary conditions for temperature

Abstract

We consider non-stationary 1-D flow of a compressible viscous heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. The homogeneous boundary conditions for velocity and microrotation, as well as non-homogeneous boundary conditions for temperature are introduced. This problem has a unique generalized solution locally in time. With the help of this result and using the principle of extension we prove a global-in-time existence theorem.