Invariant sample measures and random Liouville type theorem for the two-dimensional stochastic Navier-Stokes equations

In this article, we first prove some sufficient conditions guaranteeing the existence of invariant sample measures for random dynamical systems via the approach of global random attractors. Then we consider the two-dimensional incompressible Navier-Stokes equations with additive white noise as an ex...

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Detalles Bibliográficos
Autores: Zhao, Caidi, Wang, Jintao, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/130373
Acceso en línea:https://hdl.handle.net/11441/130373
https://doi.org/10.1016/j.jde.2022.02.007
Access Level:acceso abierto
Palabra clave:Invariant sample measures
Random Liouville type theorem
Random dynamical system
Global random attractor
Stochastic Navier-Stokes equations
Descripción
Sumario:In this article, we first prove some sufficient conditions guaranteeing the existence of invariant sample measures for random dynamical systems via the approach of global random attractors. Then we consider the two-dimensional incompressible Navier-Stokes equations with additive white noise as an example to show how to check the sufficient conditions for concrete stochastic partial differential equations. Our results generalize the Liouville type theorem to the random case and reveal that the invariance of the sample measures is a particular situation of the random Liouville type theorem