Heriot-Watt Mathematics Report Series
HWM02-58, 22 Oct 2003
Ergodic theorems for 2D statistical hydrodynamics
S.B. Kuksin
Abstract
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
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.
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