Global classical large solution to compressible viscous micropolar and heat-conducting fluids with vacuum

Zefu Feng,Changjiang Zhu

doi:10.3934/dcds.2019127

Abstract

In this paper we consider the non-stationary 1-D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. Since the strong nonlinearity and degeneracies of the equations due to the temperature equation and vanishing of density, there are a few results about global existence of classical solution to this model. In the paper, we obtain a global classical solution to the equations with large initial data and vacuum. Moreover, we get the uniqueness of the solution to this system without vacuum. The analysis is based on the assumption \begin{document}$ \kappa(\theta) = O(1+\theta^q) $\end{document} where \begin{document}$ q\geq0 $\end{document} and delicate energy estimates.

Highlights

In this paper, we consider non-stationary 1-D flow of a compressible viscous and heat-conducting micropolar fluid with vacuum, being in a thermodynamical sense perfect and polytropic
We focus on the polytropic perfect and polytropic fluids and assume that
Integrating over (0, T ) and using Corollary 3, we complete the proof of Lemma 3.7

Summary

Introduction

We consider non-stationary 1-D flow of a compressible viscous and heat-conducting micropolar fluid with vacuum, being in a thermodynamical sense perfect and polytropic. Lemma 3.6 implies the following corollary, which proof can be found in [33, 34]. Integrating over (0, T ) and using Corollary 3, we complete the proof of Lemma 3.7.

Results

Conclusion