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$L^1$-Uniqueness of Kolmogorov Operators Associated to 2D Stochastic Navier-Stokes Coriolis Equations with Space-Time White Noise
- Publication Year :
- 2013
-
Abstract
- We consider the Kolmogorov operator $K$ associated to a stochastic Navier-Stokes equation driven by space-time white noise on the two-dimensional torus with periodic boundary conditions and a rotating reference frame, introducing fictitious forces such as the Coriolis force. This equation then serves as a simple model for geophysical flows. We prove that the Gaussian measure induced by the enstrophy is infinitesimally invariant for $K$ on finitely based cylindrical test functions and moreover $K$ is $L^1$-unique w. r. t. the enstrophy measure for sufficiently large viscosity.<br />Comment: 18 pages. This is the prepublication draft of the article published online in J. Theoret. Probab (2014)
- Subjects :
- Mathematics - Probability
76D05, 60H15, 76B03, 76M35
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1304.4384
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10959-014-0582-8