数学物理学报(英文版) ›› 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

秦玉明, 宋锦萍   

  1. Department of Applied Mathematics, Donghua University, Shanghai 201620, China
  • 收稿日期:2006-11-12 修回日期:2008-01-31 出版日期:2010-01-20 发布日期:2010-01-20
  • 基金资助:

    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).

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).

摘要:

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.

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

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

中图分类号: 

  • 35Q72