One-Dimensional Compressible Viscous Micropolar Fluid Model: Stabilization of the Solution for the Cauchy Problem

We consider the Cauchy problem for nonstationary 1D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. This problem has a unique generalized solution on Rx[0, T ]for each T > 0. Supposing that the initial functions are small perturbations of the constants we derive a priori estimates for the solution independent of T, which we use in proving of the stabilization of the solution.