Acta mathematica scientia, Series B >
MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER--STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID
Received date: 2006-11-12
Revised date: 2008-01-31
Online 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).
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 δ1, δ2, … , 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.
QIN Yu-Ming , SONG Jin-Ping . MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER--STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID[J]. Acta mathematica scientia, Series B, 2010 , 30(1) : 289 -311 . DOI: 10.1016/S0252-9602(10)60046-X
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