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September  2008, 10(4): 761-781. doi: 10.3934/dcdsb.2008.10.761

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

Tomás Caraballo 1, , Peter E. Kloeden 2, and  José Real 3,

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, Germany
3. 

Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla

Received  May 2007 Revised  May 2008 Published  August 2008

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: regularity results, Globally modified Navier-Stokes equations, time-average measures., invariant measures, statistical solutions, global attractors.
Mathematics Subject Classification: 35Q30, 35K90, 37L3.
Citation: Tomás Caraballo, Peter E. Kloeden, José Real. Invariant measures and Statistical solutions of the globally modified Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2008, 10 (4) : 761-781. doi: 10.3934/dcdsb.2008.10.761
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