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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

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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