Existence and Regularity of Invariant Measures for the Three Dimensional Stochastic Primitive Equations

We establish the continuity of the Markovian semigroup associated with strong solutions of the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. The proof is based on new moment bounds for strong solutions. The invariant measure is supported on strong solutions, but is furthermore shown to have higher regularity properties.