Pullback attractors for 2D-Navier-Stokes equations with delays in continuous and sub-linear operators

Pedro Marín-Rubio; José Real

doi:10.3934/dcds.2010.26.989

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2010, Volume 26, Issue 3: 989-1006. Doi: 10.3934/dcds.2010.26.989

This issue Previous Article Optimal interior partial regularity for nonlinear elliptic systems Next Article A note on two approaches to the thermodynamic formalism

Pullback attractors for 2D-Navier-Stokes equations with delays in continuous and sub-linear operators

Pedro Marín-Rubio¹ and
José Real^2,

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

Received: May 2009

Revised: August 2009

Published: September 2010

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Abstract

We obtain a result of existence of solutions to the 2D-Navier-Stokes model with delays, when the forcing term containing the delay is sub-linear and only continuous. As a consequence of the continuity assumption the uniqueness of solutions does not hold in general. We use then the theory of multi-valued dynamical system to establish the existence of attractors for our problem in several senses and establish relations among them.

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Mathematics Subject Classification: Primary: 35B40; 35Q30; 37L30.

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Pullback attractors for 2D-Navier-Stokes equations with delays in continuous and sub-linear operators

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