Some new regularity results of pullback attractors for 2D Navier-Stokes equations with delays

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

doi:10.3934/cpaa.2015.14.1603

Article Contents

2015, Volume 14, Issue 5: 1603-1621. Doi: 10.3934/cpaa.2015.14.1603

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Some new regularity results of pullback attractors for 2D Navier-Stokes equations with delays

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

Received: March 31, 2012

Revised: June 30, 2012

Published: August 2015

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Abstract

In this paper we strengthen some results on the existence and properties of pullback attractors for a 2D Navier-Stokes model with finite delay formulated in [Caraballo and Real, J. Differential Equations 205 (2004), 271--297]. Actually, we prove that under suitable assumptions, pullback attractors not only of fixed bounded sets but also of a set of tempered universes do exist. Moreover, thanks to regularity results, the attraction from different phase spaces also happens in $C([-h,0];V)$. Finally, from comparison results of attractors, and under an additional hypothesis, we establish that all these families of attractors are in fact the same object.

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Mathematics Subject Classification: Primary: 35B41, 35Q30, 37L30.

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References

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