Maximal attractors for the compressible Navier–stokes equations of viscous and heat conductive fluid

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 is found, and the existence of maximal (universal) attractors in is established.