# American Institute of Mathematical Sciences

June  2019, 39(6): 3069-3097. doi: 10.3934/dcds.2019127

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

 School of Mathematics, South China University of Technology, Guangzhou 510641, China

* Corresponding author: Changjiang Zhu

Received  February 2018 Revised  December 2018 Published  February 2019

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 $\kappa(\theta) = O(1+\theta^q)$ where $q\geq0$ and delicate energy estimates.

Citation: Zefu Feng, Changjiang Zhu. Global classical large solution to compressible viscous micropolar and heat-conducting fluids with vacuum. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3069-3097. doi: 10.3934/dcds.2019127
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