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Ergodic theorems for 2D statistical hydrodynamics. (English) Zbl 1030.37054
Author’s summary: We consider the 2D Navier-Stokes system, perturbed by a random force, such that sufficiently many of its Fourier modes are excited (e.g. all of them are). We discuss the results on the existence and uniqueness of a stationary measure for this system, obtained in last years, homogeneity of the measures and some of their limiting properties. Next we use these results to prove that solutions of the equations obey the central limit theorem and the strong law of large numbers.
See also the work of the author [Transl., Ser. 2, Am. Math. Soc. 206, 161-176 (2002; Zbl 1023.37031)] and together with A. Shirikyan [Math. Phys. Anal. Geom. 4, 147-195 (2001; Zbl 1013.37046)].

MSC:
37L40 Invariant measures for infinite-dimensional dissipative dynamical systems
35R60 PDEs with randomness, stochastic partial differential equations
35Q30 Navier-Stokes equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76D05 Navier-Stokes equations for incompressible viscous fluids
76M35 Stochastic analysis applied to problems in fluid mechanics
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References:
[1] DOI: 10.1007/s002200100424 · Zbl 0983.60058
[2] DOI: 10.2307/121126 · Zbl 0972.35196
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