Universal Attractors¶for the Navier-Stokes Equations¶of Compressible and Heat-Conductive Fluid¶in Bounded Annular Domains in ℝn

Abstract

This paper is concerned with the dynamics for the Navier-Stokes equations for a polytropic viscous heat-conductive ideal gas in bounded annular domains Ω _n in ℝⁿ(n= 2, 3). One of the important features of this problem is that the metric spaces H ⁽¹⁾ and H ⁽²⁾ we work with are two incomplete metric spaces, as can be seen from the constraints θ >0 and u> 0, withθ and u being absolute temperature and specific volume respectively. For any constants δ₁, δ₂, δ₃, δ₄, δ₅ satisfying certain conditions, two sequences of closed subspaces H ^{( i )} _δ⊂H ^{( i )} (i= 1,2) are found, and the existence of two (maximal) universal attractors in H ⁽¹⁾ _δ and H ⁽²⁾ _δ is proved.