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

Yuming Qin; Lan Huang; Zhiyong Ma

doi:10.3934/cpaa.2009.8.1991

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2009, Volume 8, Issue 6: 1991-2012. Doi: 10.3934/cpaa.2009.8.1991

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

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

Received: October 31, 2008

Revised: March 31, 2009

Published: October 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B30, 35B40; Secondary: 35Q30.

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

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