Analysis of a stochastic 2D–Navier-Stokes model with 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....

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Detalles Bibliográficos
Autores: Liu, Linfang, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/92689
Acceso en línea:https://hdl.handle.net/11441/92689
https://doi.org/10.1007/s10884-018-9703-x
Access Level:acceso abierto
Palabra clave:Stochastic Navier-Stokes equation
Equilibrium solution
Polynomial stability
Unbounded variable delay
Descripción
Sumario: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.