Artículo
Invariant measures for stochastic 3D Lagrangian-averaged Navier–Stokes equations with infinite delay
Autor/es | Yang, Shuang
Caraballo Garrido, Tomás Li, Yangrong |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2023-04-05 |
Fecha de depósito | 2023-02-27 |
Publicado en |
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Resumen | 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, ... 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. |
Cita | Yang, S., Caraballo Garrido, T. y Li, Y. (2023). Invariant measures for stochastic 3D Lagrangian-averaged Navier–Stokes equations with infinite delay. Communications in nonlinear science and numerical simulation, 118, 107004-1. https://doi.org/10.1016/j.cnsns.2022.107004. |
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