Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions (Zurich Lectures in Advanced Mathematics) - Softcover

Sergei B. Kuksin

Softcover

ISBN 10: 3037190213 ISBN 13: 9783037190210

Verlag: EMS Press, 2006

Inhaltsangabe

The 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 the 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.

Details zur Ausgabe

• Verlag: EMS Press
• Erscheinungsdatum: 2006
• Sprache: Englisch
• ISBN 10: 3037190213
• ISBN 13: 9783037190210
• Einband: Taschenbuch
• Auflage: 1
• Anzahl der Seiten: 92
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar