# American Institute of Mathematical Sciences

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

 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.
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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