Local existence theorem for micropolar viscous real gas flow with homogeneous boundary conditions

Abstract

We consider the model for one-dimensional micropolar, viscous, polytropic, and thermally conductive real gas flow with homogeneous boundary conditions, using the generalized equation of state for pressure. The generalization is shown by the fact that the pressure depends on the mass density as a power function. The governing system of partial differential equations is given in the Lagrangian description. Using the Faedo-Galerkin method and a priori estimates, we prove that the generalized solution exists locally in time.

Large-time behavior of solutions to the compressible micropolar fluid with shear viscosity

“…For the one-dimensional case, the compressible micropolar ideal gas model was first described by Mujaković (see [31]), and then the local existence, global existence, regularity, large time behavior, stity of the solution, and the existence of global attractors for the nonisentropic compressible micropolar ideal gas model were established in [6,13,25,28,32,33,34,35,36,37,42]. Recently, there have been several investigations on the global existence, uniqueness, regularity, and large time behavior of solutions to problems associated with the compressible micropolar real gas model in [8,2,3,4,23]. In addition, for the isentropic micropolar fluid model, we would like to refer to the studies in [5].…”