 06178 Sergei B. Kuksin
 Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions
(1221K, postscript)
Jun 8, 06

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Abstract. The book gives an account of recent achievements in the mathematical
theory of twodimensional turbulence, described by the 2D NavierStokes
equation, perturbed by a random force. Main results, presented here,
were obtained during the last 510 years and can be found only in papers.
The book starts with preliminaries on partial differential equations and
on stochastic, which makes it selfcontained and available for readers
with general background in analysis. It goes on to recent
results on ergodicity of the random dynamical system which the randomly
forced NavierStokes equation defines in the function space of
divergencefree vector fields, including a Central Limit Theorem. The physical meaning of these results is discussed as well as their relations with the theory of attractors. Next the author studies behaviour of solutions when the viscosity goes to zero. The final section presents the balance relations  the infinitelymany explicit algebraical relations, satisfied by the solutions  and their discussion.
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