a1 Department of Mathematics, University of Surrey Guildford, GU2 7XH, United Kingdom e-mail: email@example.com
The weighted energy theory for Navier-Stokes equations in 2D strips is developed. Based on this theory, the existence of a solution in the uniformly local phase space (without any spatial decaying assumptions), its uniqueness and the existence of a global attractor are verified. In particular, this phase space contains the 2D Poiseuille flows.
(Received March 23 2007)
(Accepted May 24 2007)
This work is partially supported by Alexander von Humboldt foundation and by the CRDF grant RUM1- 2654-MO-05. The author is also grateful to A. Afendikov M. Efendiev and A. Mielke for stimulating discussions.