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

Zefu Feng; Changjiang Zhu

doi:10.3934/dcds.2019127

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2019, Volume 39, Issue 6: 3069-3097. Doi: 10.3934/dcds.2019127

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

Zefu Feng and
Changjiang Zhu^,

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

^* Corresponding author: Changjiang Zhu
^* Corresponding author: Changjiang Zhu

Received: February 2018

Revised: December 2018

Published: February 2019

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

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Mathematics Subject Classification: Primary: 35Q35, 35B65; Secondary: 76N10.

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References

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