Propagation of oscillations, complete trajectories and attractors for compressible flows

Abstract

We study the qualitative properties and the long time behaviour of the finite energy weak solutions to the Navier-Stokes equations of compressible flows. Under certain restrictions imposed on the adiabatic constant γ, the existence of global compact attractors as well as other results on stabilization are obtained. 2000 Mathematics Subject Classification: 35Q30, 35B41.

On the Long-Time Behaviour of Compressible Fluid Flows Subjected to Highly Oscillating External Forces

“…Related results may be found in [2], Novotný and Straškraba [14], and also Straškraba [15]. Similar problems for mixtures of two incompressible fluids were considered by Gerbeau and Le Bris [11].…”

“…All details of the above mentioned procedure can be found in [2], [8]. Adapting [2, Proposition 3.1] to the present situation, we deduce the following result:…”

“…Now, it is proved in [8] (see also [2,Section 2]) that D is a uniformly bounded and continuous function on the whole real line t ∈ % and, moreover, it satisfies…”