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

Gaussian invariant measures and stationary solutions of 2D Primitive Equations