A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions

By Tomás Caraballo, Xiaoying Han. 2015

52 citations recorded by the source corpus.

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.

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

View Paper: https://www.semanticscholar.org/paper/e220e753f3be870474b65ab214d300e416386ed4

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

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”
Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in $(1/2,1)$ (2017, background): “To name only a few, some recent papers are [3], [22], [23] .”