Zurich Lectures in Advanced Mathematics 2006; 104 pp; softcover Volume: 3 ISBN10: 3037190213 ISBN13: 9783037190210 List Price: US$34 Member Price: US$27.20 Order Code: EMSZLEC/3
 This 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. 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 selfcontained 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 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 the behaviour of solutions when the viscosity goes to zero. In the final section these dynamical methods are used to derive the socalled balance relationsthe 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. Readership Graduate students and research mathematicians interested in mathematical physics and differential equations Table of Contents  Function spaces
 The deterministic 2D NavierStokes Equation
 Random kickforces
 Whiteforced equations
 Preliminaries from measure theory
 Uniqueness of a stationary measure: kickforces
 Uniqueness of a stationary measure: whiteforces
 Ergodicity and the strong law of large numbers
 The martingale approximation and CLT
 The Eulerian limit
 Balance relations for the whiteforced NSE
 Comments
 Bibliography
 Index
