Exponential stability in H^4 for the Navier--Stokes equations of compressible and heat conductive fluid

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September 2005, 4(3): 635-664. doi: 10.3934/cpaa.2005.4.635

Exponential stability in $H^4$ for the Navier--Stokes equations of compressible and heat conductive fluid

Yuming Qin ^1, , T. F. Ma ^2, , M. M. Cavalcanti ^2, and D. Andrade ^2,

1.	Department of Mathematics - Henan University,Kaifeng 475001, China
2.	Department of Mathematics - State University of Maringá, 87020-900 Maringá, PR, Brazil, Brazil, Brazil

Received June 2004 Revised April 2005 Published June 2005

Abstract
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This paper is concerned with the exponential stability of solutions in $H^4$ for the Navier--Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains $\Omega_n$ in $\mathbb{R}^n (n=2,3)$.

Keywords: Compressible Navier--Stokes equation, spherically symmetric solutions., polytropic viscous ideal gas.

Mathematics Subject Classification: Primary: 35B30, 35B40; Secondary: 35Q7.

Citation: Yuming Qin, T. F. Ma, M. M. Cavalcanti, D. Andrade. Exponential stability in $H^4$ for the Navier--Stokes equations of compressible and heat conductive fluid. Communications on Pure & Applied Analysis, 2005, 4 (3) : 635-664. doi: 10.3934/cpaa.2005.4.635

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