Asymptotic behaviour and attractors of 2D-Navier-Stokes models with delays
by
Tomás Caraballo
University of Seville
Coauthors: José Real

In this work we analyse the long-time behaviour of a 2D-Navier-Stokes model containing some hereditary characteristics in the forcing term. When the viscosity is large enough, we prove that all solutions approach the unique stationary solution exponentially fast. Then, when the viscosity is small, we prove the existence of a global attractor for the model. The main technique used to prove the existence of this attracting set is the theory of pullback attractor which has proven very useful in dealing with nonautonomous dynamical systems. We emphasise that, when one considers a constant delay in the model the classical theory of global attractors can be properly adapted to handle the problem, but when the delay appearing in the forcing term is, for instance, variable, the problem can be modeled by using an abstract nonautonomous functional partial differential equation which generates a nonautonomous dynamical system.

Date received: May 29, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calo-22.