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The attractor of a Navier-Stokes system in an unbounded channel-like domain. (English) Zbl 0762.35082

(Author’s summary.) 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 attractor 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.

MSC:

35Q30 Navier-Stokes equations
35B40 Asymptotic behavior of solutions to PDEs
37C75 Stability theory for smooth dynamical systems
76D05 Navier-Stokes equations for incompressible viscous fluids
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