Regularity of pullback attractors and attraction in $H^1$ in arbitrarily large finite intervals for 2D Navier-Stokes equations with infinite delay

Julia García-Luengo; Pedro Marín-Rubio; José Real

doi:10.3934/dcds.2014.34.181

Article Contents

2014, Volume 34, Issue 1: 181-201. Doi: 10.3934/dcds.2014.34.181

This issue Previous Article Longtime behavior of nonlocal Cahn-Hilliard equations Next Article Pullback attractors for the non-autonomous 2D Navier--Stokes equations for minimally regular forcing

Regularity of pullback attractors and attraction in $H^1$ in arbitrarily large finite intervals for 2D Navier-Stokes equations with infinite delay

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

Received: September 30, 2012

Revised: January 31, 2013

Published: December 2013

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Abstract

In this paper we strengthen some results on the existence and properties of pullback attractors for a non-autonomous 2D Navier-Stokes model with infinite delay. Actually we prove that under suitable assumptions, and thanks to regularity results, the attraction also happens in the $H^1$ norm for arbitrarily large finite intervals of time. Indeed, from comparison results of attractors we establish that all these families of attractors are in fact the same object. The tempered character of these families in $H^1$ is also analyzed.

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Mathematics Subject Classification: 35B41, 35B65, 35Q30, 35R10.

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