Pullback V-attractors of the 3-dimensional globally modified Navier-Stokes equations

P.E. Kloeden; José A. Langa; José Real

doi:10.3934/cpaa.2007.6.937

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2007, Volume 6, Issue 4: 937-955. Doi: 10.3934/cpaa.2007.6.937

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Pullback V-attractors of the 3-dimensional globally modified Navier-Stokes equations

1.
FB Mathematik, Johann Wolfgang Goethe Universität, Postfach 11 19 32, D-60054 Frankfurt a.M.
2.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
3.
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla

Received: November 2006

Revised: May 2007

Published: December 2007

Abstract / Introduction Related Papers Cited by

Abstract

The existence and finite fractal dimension of a pullback attractor in the space $V$ for a three dimensional system of the nonautonomous Globally Modified Navier-Stokes Equations on a bounded domain is established under appropriate properties on the time dependent forcing term. These equations were proposed recently by Caraballo et al and are obtained from the Navier- Stokes Equations by a global modification of the nonlinear advection term. The existence of the attractor is obtained via the flattening property, which is verified.

Keywords:

3-dimensional Navier-Stokes equations,
weak solutions,
existence and uniqueness of strong solutions,
flattening property,
nonautonomous and pullback attractors.

Mathematics Subject Classification: 35Q30, 35K90, 37L30.

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