Pullback attractors for globallymodified Navier-Stokes equations with infinite delays

Pedro Marín-Rubio; Antonio M. Márquez-Durán; José Real

doi:10.3934/dcds.2011.31.779

Article Contents

2011, Volume 31, Issue 3: 779-796. Doi: 10.3934/dcds.2011.31.779

This issue Previous Article Hopf bifurcation for some analytic differential systems in $\R^3$ via averaging theory Next Article Global bifurcation and stable two-phase separation for a phase field model in a disk

Pullback attractors for globally modified Navier-Stokes equations with infinite delays

1.
Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla
2.
Departamento de 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 30, 2009

Revised: May 31, 2011

Published: August 2011

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Abstract

We establish the existence of pullback attractors for the dynamical system associated to a globally modified model of the Navier-Stokes equations containing delay operators with infinite delay in a suitable weighted space. Actually, we are able to prove the existence of attractors in different classes of universes, one is the classical of fixed bounded sets, and the other is given by a tempered condition. Relationship between these two kind of objects is also analyzed.

Keywords:

Globally Modified Navier-Stokes Equations; pullback attractors; infinite delays.

Mathematics Subject Classification: Primary: 35K55, 35Q30, 34D45.

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References

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