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Lp‐uniqueness of Kolmogorov operators associated with 2D‐stochastic Navier‐Stokes‐Coriolis equations

We prove that the Kolmogorov operator associated with stochastic Navier‐Stokes‐Coriolis equations on the 2D‐Torus is m‐dissipative in the space Lp(μ) for any p ∈ [1, ∞[, where μ is an infinitesimally invariant measure. The proof is based on exponential moment estimates on μ related to the enstrophy and pointwise gradient estimates on the transition semigroup induced by finite dimensional approximations.