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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

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