Caraballo, Tomás; Han, Xiaoying A survey on Navier-Stokes models with delays: existence, uniqueness and asymptotic behavior of solutions. (English) Zbl 1406.35221 Discrete Contin. Dyn. Syst., Ser. S 8, No. 6, 1079-1101 (2015). Summary: In this survey paper we review several aspects related to Navier-Stokes models when some hereditary characteristics (constant, distributed or variable delay, memory, etc) appear in the formulation. First some results concerning existence and/or uniqueness of solutions are established. Next the local stability analysis of steady-state solutions is studied by using the theory of Lyapunov functions, the Razumikhin-Lyapunov technique and also by constructing appropriate Lyapunov functionals. A Gronwall-like lemma for delay equations is also exploited to provide some stability results. In the end we also include some comments concerning the global asymptotic analysis of the model, as well as some open questions and future lines for research. Cited in 31 Documents MSC: 35Q30 Navier-Stokes equations 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 35B40 Asymptotic behavior of solutions to PDEs 37H10 Generation, random and stochastic difference and differential equations 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:Navier-Stokes equations; Galerkin; stability; variable delay; distributed delay; measurable delay PDFBibTeX XMLCite \textit{T. Caraballo} and \textit{X. Han}, Discrete Contin. Dyn. Syst., Ser. S 8, No. 6, 1079--1101 (2015; Zbl 1406.35221) Full Text: DOI References: [1] M. Anguiano, Pullback attractors for nonautonomous dynamical systems,, Differential and Difference Eqns. with Apps., 47, 217 (2013) · Zbl 1332.37056 [2] A. V. 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