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

 

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Opened Access A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions
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Author: Caraballo Garrido, Tomás
Xiaoying, Han
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2015
Published in: Discrete and Continuous Dynamical Systems - Series S, 8(6), 1079-1101
Document type: Article
Abstract: 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.
Cite: Caraballo Garrido, T. y Xiaoying, H. (2015). A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions. Discrete and Continuous Dynamical Systems - Series S, 8 (6), 1079-1101.
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URI: http://hdl.handle.net/11441/32694

DOI: http://dx.doi.org/10.3934/dcdss.2015.8.1079

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