Global existence and exponential stability in H^4 for the nonlinear compressible Navier-Stokes equations

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November 2009, 8(6): 1991-2012. doi: 10.3934/cpaa.2009.8.1991

Global existence and exponential stability in $H^4$ for the nonlinear compressible Navier-Stokes equations

Yuming Qin ^1, , Lan Huang ^2, and Zhiyong Ma ^2,

1.	Department of Applied Mathematics, Donghua University, Shanghai 201620, China
2.	College of Information Science and Technology, Donghua University, Shanghai 201620

Received November 2008 Revised April 2009 Published August 2009

Abstract
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This paper is concerned with the global existence and exponential stability of weak solutions in $H^4$ for a real viscous heat-conducting flow with shear viscosity in a bounded domain $\Omega=(0,1)$ . Some new ideas and more delicate estimates are introduced to prove these results.

Keywords: shear viscosity., a uniform priori estimates, Global existence, exponential stability.

Mathematics Subject Classification: Primary: 35B30, 35B40; Secondary: 35Q3.

Citation: Yuming Qin, Lan Huang, Zhiyong Ma. Global existence and exponential stability in $H^4$ for the nonlinear compressible Navier-Stokes equations. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1991-2012. doi: 10.3934/cpaa.2009.8.1991

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