A shear flow problem for compressible viscous and heat conducting micropolar fluid: local existence theorem
Ivan Dražić, Nermina Mujaković · 2017
We consider the non-stationary 3-D flow of a compressible and viscous heat-conducting micropolar fluid in the domain bounded by two parallel horizontal plates that present solid thermoinsulated walls. In the thermodynamical sense the fluid is perfect and polytropic, and we assume that the initial density and initial temperature are strictly positive. In this work we present the local existence result for corresponding one-dimensional problem in Lagrangian description with smooth enough initial data and non-homogeneous boundary data for velocity, as well as homogeneous boundary data for microrotation and heat flux. The proof is based on Faedo-Galerkin method.