Gaussian invariant measures and stationary solutions of 2D Primitive Equations

Abstract

We introduce a Gaussian measure formally preserved by the 2-dimensional Primitive Equations driven by additive Gaussian noise. Under such measure the stochastic equations under consideration are singular: we propose a solution theory based on the techniques developed by Gubinelli and Jara in \cite{GuJa13} for a hyperviscous version of the equations.

15 pages

References in corpus (4)

• Existence and Regularity of Invariant Measures for the Three Dimensional Stochastic Primitive Equations
• Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness
• Partial and full hyper-viscosity for Navier-Stokes and primitive equations
• Hyperviscous stochastic Navier-Stokes equations with white noise invariant measure in two dimensions

Cited by in corpus (1)

• On the infinite dimension limit of invariant measures and solutions of Zeitlin's 2D Euler equations