Article
Analysis of a stochastic 2D–Navier-Stokes model with infinite delay
Author/s | Liu, Linfang
Caraballo Garrido, Tomás |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2019-12 |
Deposit Date | 2020-02-03 |
Published in |
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Abstract | Some results concerning a stochastic 2D Navier-Stokes system when the external forces contain hereditary characteristics are established. The existence and uniqueness of solutions in the case of unbounded (infinite) delay ... Some results concerning a stochastic 2D Navier-Stokes system when the external forces contain hereditary characteristics are established. The existence and uniqueness of solutions in the case of unbounded (infinite) delay are first proved by using the classical technique of Galerkin approximations. The local stability analysis of constant solutions (equilibria) is also carried out by exploiting two approaches. Namely, the Lyapunov function method and by constructing appropriate Lyapunov functionals. The asymptotic stability and hence, the uniqueness of equilibrium solution are obtained by constructing Lyapunov functionals. Moreover, some sufficient conditions ensuring the polynomial stability of the equilibrium solution in a particular case of unbounded variable delay will be provided. Exponential stability for other special cases of infinite delay remains as an open problem. |
Project ID. | MTM2015-63723-P
P12-FQM-1492 11671142 11371087 11571125 |
Citation | Liu, L. y Caraballo Garrido, T. (2019). Analysis of a stochastic 2D–Navier-Stokes model with infinite delay. Journal of Dynamics and Differential Equations, 31 (4), 2249-2274. |
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