The attractor of a Navier-Stokes system in an unbounded channel-like domain

Abstract

The Navier-Stokes system describes a flow of a fluid in an unbounded planar channel-like domain. It is proved that in the case when an external force decays at infinity, the semigroup generated by this system has a global attractor and its Hausdorff dimension is finite. Estimates in weighted Sobolev spaces are used as a main tool. Asymptotics, as the distance from the origin in the plane tends to infinity, of functions on the attactor is found. This asymptotics show that all dynamics on the attractor decays at infinity and the turbulence generated by the force does not propagate to infinity.