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September  2010, 26(3): 989-1006. doi: 10.3934/dcds.2010.26.989

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

Pedro Marín-Rubio 1, 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  December 2009

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.
Keywords: delay terms, Navier-Stokes equations, pullback attractors, tempered attractors..
Mathematics Subject Classification: Primary: 35B40; 35Q30; 37L3.
Citation: Pedro Marín-Rubio, José Real. Pullback attractors for 2D-Navier-Stokes equations with delays in continuous and sub-linear operators. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 989-1006. doi: 10.3934/dcds.2010.26.989
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