Title: Randomly Forced Nonlinear Pdes and Statistical Hydrodynamics in 2 Space Dimensions (Zurich Lectures in Advanced Mathematics) (Zurich Lectures in Advanced Mathematics)
Publisher: European Mathematical Society
Publication Date: 2006
Language: English
ISBN 10: 3037190213
ISBN 13: 9783037190210
Binding: Paperback
Condition: Brand New
Weight: 0.36 kilograms

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Synopsis

This book gives an account of recent achievements in the mathematical theory of two-dimensional turbulence, described by the 2D Navier-Stokes equation, perturbed by a random force. The main results presented here were obtained during the last five to ten years and, up to now, have been available only in papers in the primary literature. Their summary and synthesis here, beginning with some preliminaries on partial differential equations and stochastics, make this book a self-contained account that will appeal to readers with a general background in analysis. After laying the groundwork, the author goes on to recent results on ergodicity of random dynamical systems, which the randomly forced Navier-Stokes equation defines in the function space of divergence-free 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 the behaviour of solutions when the viscosity goes to zero. In the final section these dynamical methods are used to derive the so-called balance relations--the infinitely many algebraical relations satisfied by the solutions. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

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