Recurrent motions in the nonautonomous Navier-Stokes system

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May 2003, 3(2): 255-262. doi: 10.3934/dcdsb.2003.3.255

Recurrent motions in the nonautonomous Navier-Stokes system

Vena Pearl Bongolan-walsh ^1, , David Cheban ^2, and Jinqiao Duan ^1,

1.	Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, United States, United States
2.	State University of Moldova, Department of Mathematics and Informatics, A. Mateevich Street 60, MD–2009 Chişinău, Moldavia

Received June 2002 Revised December 2002 Published February 2003

Abstract
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We prove the existence of recurrent or Poisson stable motions in the Navier-Stokes fluid system under recurrent or Poisson stable forcing, respectively. We use an approach based on nonautonomous dynamical systems ideas.

Keywords: Navier-Stokes equations, Nonautonomous dynamical system, skew-product flow, Poisson stable motion., recurrent motion.

Mathematics Subject Classification: Primary: 34C35, 34D20, 58F10, 58F12; Secondary: 35B35, 35B4.

Citation: Vena Pearl Bongolan-walsh, David Cheban, Jinqiao Duan. Recurrent motions in the nonautonomous Navier-Stokes system. Discrete & Continuous Dynamical Systems - B, 2003, 3 (2) : 255-262. doi: 10.3934/dcdsb.2003.3.255

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