Nonhomogeneous Boundary Value Problem for One-Dimensional Compressible Viscous Micropolar Fluid Model: Regularity of the Solution

Nermina Mujaković

doi:10.1155/2008/189748

Abstract

An initial-boundary value problem for 1D flow of a compressible viscous heat-conducting micropolar fluid is considered; the fluid is thermodynamically perfect and polytropic. Assuming that the initial data are Holder continuous on and transforming the original problem into homogeneous one, we prove that the state function is Holder continuous on , for each . The proof is based on a global-in-time existence theorem obtained in the previous research paper and on a theory of parabolic equations.

Highlights

In this paper, we consider a nonstationary 1D flow of a compressible viscous and heatconducting micropolar fluid, being in a thermodynamical sense perfect and polytropic
In 1–3, we considered the problem with homogeneous boundary conditions
As in 4, 5, the case of nonhomogeneous boundary conditions for velocity and microrotation which is called in gas dynamics “problem on piston” see 6

Summary

Recommended by Michel Chipot

An initial-boundary value problem for 1D flow of a compressible viscous heat-conducting micropolar fluid is considered; the fluid is thermodynamically perfect and polytropic. Assuming that the initial data are Holder continuous on 0, 1 and transforming the original problem into homogeneous one, we prove that the state function is Holder continuous on 0, 1 × 0, T , for each T > 0. The proof is based on a global-in-time existence theorem obtained in the previous research paper and on a theory of parabolic equations.

Introduction

Hxα Dtmf

Using the inequalities