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We consider the Kolmogorov operator $K$ associated to a stochasticNavier-Stokes equation driven by space-time white noise on the two-dimensionaltorus with periodic boundary conditions and a rotating reference frame,introducing fictitious forces such as the Coriolis force. This equation thenserves as a simple model for geophysical flows. We prove that the Gaussianmeasure induced by the enstrophy is infinitesimally invariant for $K$ onfinitely based cylindrical test functions and moreover $K$ is $L^1$-unique w.r. t. the enstrophy measure for sufficiently large viscosity.

$L^1$-Uniqueness of Kolmogorov Operators Associated to 2D Stochastic Navier-Stokes Coriolis Equations with Space-Time White Noise