Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (1): 289-311.doi: 10.1016/S0252-9602(10)60046-X

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MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER--STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID

 QIN Yu-Ming, SONG Jin-Ping   

  1. Department of Applied Mathematics, Donghua University, Shanghai 201620, China
  • Received:2006-11-12 Revised:2008-01-31 Online:2010-01-20 Published:2010-01-20
  • Supported by:

    This work was supported in part by the NSF of China (10571024, 10871040) and the grant of Prominent Youth
    of Henan Province of China (0412000100).

Abstract:

This article is concerned with the existence of maximal attractors in Hi (i=1,2,4) for the compressible Navier--Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn (n=2,3). One of the important features is that the metric spaces H(1), H(2), and H(4) we work with are three  incomplete
metric spaces, as can be seen from the constraints θ >0 and u>0, with θ and u being absolute temperature and specific volume respectively. For any constants δ1δ2… δ8 verifying some conditions, a sequence of closed subspaces Hδ(i)    H(i) ;(i=1, 2, 4) is found, and the existence of maximal (universal) attractors in Hδ(i); (i=1, 2, 4) is
established.

Key words: compressible Navier--Stokes equations, polytropic viscous ideal gas, spherically symmetric solutions, absorbing set, maximal attractor

CLC Number: 

  • 35Q72
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