Almost Periodic Solutions and Global Attractors of Non-autonomous Navier-Stokes Equations

Details Almost Periodic Solutions and Global Attractors of Non-autonomous Navier-Stokes Equations Almost Periodic Solutions and Global Attractors of Non-autonomous Navier-Stokes Equations

2004-09-13

arxiv.org/abs/math/0409215v1

Mathematics

Dynamical Systems

J. Dynamics and Diff. Eqns., in press, 2004

Scientific paper

10.1023/B:JODY.0000041279.25095.

The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier-Stokes equations. Third, a criterion for the existence of almost periodic (quasi periodic,almost automorphic, recurrent, pseudo recurrent) solutions of non-autonomous Navier-Stokes equations is given. Finally, the authors have derived a global averaging principle for non-autonomous Navier-Stokes equations.

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