Long Time Behavior of the Stochastic 2D Navier-Stokes Equations

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Abstract

We review some basic results on existence and uniqueness of the invariant measure for the two-dimensional stochastic Navier-Stokes equations. A large part of the literature concerns the additive noise case; after revising these models, we consider our recent result [Ferrario and Zanella, Discrete Contin. Dyn. Syst. 44(1), 2024] with a multiplicative noise.

Keywords:

Two dimensional stochastic Navier-Stokes equations invariant measure multiplicative noise degenerate noise

Author Biographies

  • Benedetta Ferrario

    Dipartimento di Scienze Economiche e Aziendali, Università di Pavia, 27100 Pavia, Italy

  • Margherita Zanella

    Department of Mathematics, Politecnico di Milano, 20133 Milano, Italy

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DOI

10.4208/cmaa.2025-0016