Glasgow Mathematical Journal

Research Article

SPATIALLY NONDECAYING SOLUTIONS OF THE 2D NAVIER-STOKES EQUATION IN A STRIP

SERGEY ZELIKa1

a1 Department of Mathematics, University of Surrey Guildford, GU2 7XH, United Kingdom e-mail: s.zelik@surrey.ac.uk

Abstract

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)

Key Words:

  • 35Q30;
  • 37L30;
  • 76D03;
  • 76D05

Footnotes

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.