Pullback Attractors for 2D Navier-Stokes Equations with Delays and Their Regularity

By Julia García-Luengo, Pedro Marín-Rubio, José Real. 2013

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Abstract In this paper we obtain some results on the existence of solution, and of pullback attractors, for a 2D Navier-Stokes model with finite delay studied in [4] and [6]. Actually, we prove a result of existence and uniqueness of solution under less restrictive assumptions than in [4]. More precisely, we remove a condition on square integrable control of the memory terms, which allows us to consider a bigger class of delay terms (for instance, just under a measurability condition on the delay function leading the delayed time). After that, we deal with dynamical systems in suitable phase spaces within two metrics, the L2 norm and the H1 norm. Moreover, we prove that under these assumptions, pullback attractors not only of fixed bounded sets but also of a set of tempered universes do exist. Finally, from comparison results of attractors we establish relations among them, and under suitable additional assumptions we conclude that these families of attractors are in fact the same object.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/70652cca0c65cb1f2d43d0993b30b22aec0f5507

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In Applied Mathematics

In Control and Systems Engineering

Citations in the corpus

Stability results for 2D Navier–Stokes equations with unbounded delay (2018, background): “In the papers [22, 33, 29, 34, 30, 31, 35, 19, 32, 20, 18, 21] the authors have discussed the asymptotic behavior and regularity of solutions of 2D Navier-Stokes equations (and 3D-variations of Navier-Stokes models) with delay (finite and infinite).”