Attractors for 2D-Navier–Stokes models with delays☆

By Tomás Caraballo, José Real. 2004

277 citations recorded by the source corpus.

Abstract The existence of an attractor for a 2D-Navier–Stokes system with delay is proved. The theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous. However, on some occasions, the attractors may attract not only in the pullback sense but in the forward one as well. Also, this formulation allows to treat, in a unified way, terms containing various classes of delay features (constant, variable, distributed delays, etc.). As a consequence, some results for the autonomous model are deduced as particular cases of our general formulation.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/0207c4a68d4c6c5e8793c0ae5ab5f4946c17e6ed

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In Computational Theory and Mathematics

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Citations in the corpus

Asymptotic behaviour of two–dimensional Navier–Stokes equations with delays (2003, methodology): “This problem is being analysed by the authors and will result in the forthcoming paper Caraballo & Real (2003).”
Three dimensional system of globally modified Navier-Stokesequations with infinite delays (2010, background): “[5, 6, 7], and for ODEs and PDEs with unbounded delay terms cf.”
Asymptotic Behaviour of 2D-Navier-Stokes Equations with Delays (2003, background): “This problem is being analysed actually by the authors and will result in the forthcoming paper Caraballo et al. (2003).”
Pullback Attractors for 2D Navier-Stokes Equations with Delays and Their Regularity (2013, methodology): “The study of Navier-Stokes models including delay terms –existence, uniqueness, stationary solutions, exponential decay, and other asymptotic properties such as the existence of attractors– was initiated in the references [4, 5, 6], and after that, many different questions and models have been addre”
Method of Lyapunov functionals construction in stability of delay evolution equations (2007, methodology): “Although this model has already been analysed in details in [6–8], there are some situations which still have not been considered in those works.”
Navier–Stokes equations with delays on unbounded domains (2006, methodology): “To our knowledge, this has been rarely treated in the context of Navier-Stokes equations (cf. Caraballo & Real 2001, 2003, 2004).”
Non--autonomous and random attractors for delay random semilinear equations without uniqueness (2008, background): “[14], [7], [6], [15], [26]) or others with non-uniqueness of solutions or modelled by differential inclusions (Caraballo et al.”
Attractors for differential equations with unbounded delays (2007, unknown): “~ U(t; s; (u0; )) = (u(t; s; (u0; ); ut( ; s; (u0; )))) as in [10] since we are dealing all the time with continuous functions.”