Invariant measures for stochastic 3D Lagrangian-averaged Navier–Stokes equations with infinite delay

In this paper we investigate stochastic dynamics and invariant measures for stochastic 3D Lagrangian-averaged NavierStokes (LANS) equations driven by infinite delay and additive noise. We first use the Galerkin approximations, a priori estimates and standard Gronwall lemma to show the well-posedness...

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Detalles Bibliográficos
Autores: Yang, Shuang, Caraballo Garrido, Tomás, Li, Yangrong
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/143011
Acceso en línea:https://hdl.handle.net/11441/143011
https://doi.org/10.1016/j.cnsns.2022.107004
Access Level:acceso abierto
Palabra clave:Stochastic 3D Lagrangian-averaged Navier–Stokes equations
Infinite delay
Random attractors
Invariant measures
Generalized Banach limit
Descripción
Sumario:In this paper we investigate stochastic dynamics and invariant measures for stochastic 3D Lagrangian-averaged NavierStokes (LANS) equations driven by infinite delay and additive noise. We first use the Galerkin approximations, a priori estimates and standard Gronwall lemma to show the well-posedness for the corresponding random equation, whose solution operators lead to the existence of a random dynamical system. Next, the asymptotic compactness for the random dynamical system is established via the Ascoli-Arzel`a theorem. Besides, we derive the existence of a global random attractor for the random dynamical system. Moreover, we prove that the random dynamical system is bounded and continuous with respect to the initial time. Eventually, we construct a family of invariant Borel probability measures, which is supported by the global random attractor.