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

Nermina Mujaković

doi:10.1155/2010/796065

Abstract

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 for each . Supposing that the initial functions are small perturbations of the constants we derive a priori estimates for the solution independent of , which we use in proving of the stabilization of the solution.

Highlights

In this paper we consider the Cauchy problem for nonstationary 1D flow of a compressible viscous and heat-conducting micropolar fluid
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
In the last part we prove that the solution of our problem converges uniformly on R to a stationary one

Summary

Nermina Mujakovic

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 R× 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

Introduction

Boundary Value Problems

Dt ρ