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Randomly forced nonlinear PDEs and s...

Kuksin, Sergei B.,

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Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions/ Sergei B. Kuksin
Author:	Kuksin, Sergei B.,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2006,
Description:	1 online resource (102 pages)
Subject:	Differential equations -
Online resource:	https://doi.org/10.4171/021
Online resource:	https://www.ems-ph.org/img/books/kuksin_mini.jpg
ISBN:	9783037195215

Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions
Kuksin, Sergei B.,

Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions[electronic resource] /Sergei B. Kuksin - Zuerich, Switzerland :European Mathematical Society Publishing House,2006 - 1 online resource (102 pages) - Zurich Lectures in Advanced Mathematics (ZLAM).

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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.

ISBN: 9783037195215

Standard No.: 10.4171/021doiSubjects--Topical Terms:

704075
Differential equations

Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions
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520 $a 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.
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