Some Properties of a Generalized Solution for Shear Flow of a Compressible Viscous Micropolar Fluid Model

Abstract

We consider the non-stationary shear flow of a compressible viscous and heat-conducting micropolar fluid between two parallel plates that present solid thermoinsulated walls, whereby the lower plate is fixed and the upper one is moving irrotationally. 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 smooth initial functions and analyze the corresponding problem with non-homogeneous boundary data for velocity and homogeneous boundary data for microrotation and heat flux.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 uniqueness of the solution.