Invariant measures and Statistical solutions of the globally modified Navier-Stokes equations

Tomás Caraballo; Peter E. Kloeden; José Real

doi:10.3934/dcdsb.2008.10.761

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2008, Volume 10, Issue 4: 761-781. Doi: 10.3934/dcdsb.2008.10.761

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Invariant measures and Statistical solutions of the globally modified Navier-Stokes equations

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
2.
Institut für Mathematik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main
3.
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla

Received: April 30, 2007

Revised: April 30, 2008

Published: August 2008

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Abstract

We obtain regularity results for solutions of the three dimensional system of globally modified Navier-Stokes equations, and we investigate the relationship between global attractors, invariant measures, time-average measures and statistical solutions of these system in the case of temporally independent forcing.

Keywords:

Globally modified Navier-Stokes equations,
regularity results,
global attractors,
invariant measures,
statistical solutions,
time-average measures.

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

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