Navier-Stokes equations with delays

By Tomás Caraballo, José Real. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2001

152 citations recorded by the source corpus.

Some results on the existence and uniqueness of solutions to Navier–;Stokes equations when the external force contains some hereditary characteristics are proved.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/c875a678d31d8983ff332b3fd590e956b3a2d04e

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In Applied Mathematics

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Citations in the corpus

Stability results for 2D Navier–Stokes equations with unbounded delay (2018, methodology): “The analysis of the Navier-Stokes equations with hereditary terms was initiated by Caraballo and Real in [14], and developed in [11, 12, 13, 7, 15, 8, 9, 10, 5, 6], where several issues have been investigated: the existence and uniqueness of solution, stationary solution, the existence of attractors”
Navier–Stokes equations with delays on unbounded domains (2006, methodology): “Article submitted to Nonlinear Analysis TMA Proof. a) Uniqueness for N = 2 follows as the case with bounded domain given in Theorem 2.1 in [Caraballo & Real 2001] and it is reproduced here for the sake of completeness.”
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, methodology): “Observe that this situation is within our framework and satisfies our assumptions (Conditions (I)-(V)) ensuring the existence and uniqueness of solutions (see Caraballo & Real 2001).”
Asymptotic behaviour of two–dimensional Navier–Stokes equations with delays (2003, methodology): “In our recent work (Caraballo & Real 2001), we considered a Navier–Stokes model in which the external force contains some hereditary features and prove the existence of weak solutions.”
Pullback Attractors for 2D Navier-Stokes Equations with Delays and Their Regularity (2013, methodology): “In fact, in the theorem below, we neither assume hypotheses (IV) nor (V) of [4].”
A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions (2015, methodology): “As it was proved in the last section, conditions (I)-(IV) and (V) hold and, consequently, we can ensure the existence and uniqueness of solutions (see Caraballo and Real [11] and also the existence of strong solutions according to Theorem 3.”