Probabilistic Methods in Fluids: Proceedings of the Swansea 2002 Workshop Wales, Uk 14 - 19 April 2002

by Davies, I. M.; Jacob, N.; Truman, A.; Hassan, O.; Morgan, K.; Weatherill, Nigel P.; PROBABILISTIC METHODS IN FLUIDS WORKSHOP

• ISBN13: 9789812382269
• ISBN10: 9812382267
• Format: Hardcover
• Copyright: 2003-08-01
• Publisher: World Scientific Pub Co Inc

Summary

This volume contains recent research papers presented at the international workshop on "Probabilistic Methods in Fluids" held in Swansea. The central problems considered were turbulence and the NavierStokes equations but, as is now well known, these classical problems are deeply intertwined with modern studies of stochastic partial differential equations, jump processes and random dynamical systems. The volume provides a snapshot of current studies in a field where the applications range from the design of aircraft through the mathematics of finance to the study of fluids in porous media.

Table of Contents

Preface	vii
IRIMA	ix
Participants	xi
Sergio Albeverio and Yana Belopolskaya	1	(21)
Probabilistic Approach to Hydrodynamic Equations
Hakima Bessaih and Franco Flandoli	22	(13)
A Mean Field Result for 3D Vortex Filaments
Björn Böttcher and Niels Jacob	35	(13)
Remarks on Meixner-type Processes
Zdzislaw Brzezniak	48	(22)
Some Remarks on Ito and Stratonovich Integration in 2-smooth Banach Spaces
Thomas Caraballo	70	(14)
The Long-time Behaviour of Stochastic 2D-Navier-Stokes Equations
Pao-Liu Chow	84	(13)
Semilinear Stochastic Wave Equations
Nigel J. Cutland	97	(18)
Stochastic Navier-Stokes Equations: Loeb Space Techniques & Attractors
Arnaud Debussche	115	(15)
The 2D-Navier-Stokes Equations Perturbed by a Delta Correlated Noise
Sergio Albeverio and Benedetta Ferrarlo	130	(14)
Invariant Measures of Lévy-Khinchine Type for 2D Fluids
Franco Flandoli	144	(17)
Some Remarks on a Statistical Theory of Turbulent Flows
Christophe Giraud	161	(18)
Some Properties of Burgers Turbulence with White Noise Initial Conditions
Yuri E. Gliklikh	179	(12)
Deterministic Viscous Hydrodynamics via Stochastic Processes on Groups of Diffeomorphisms
Niels Jacob and Aubrey Truman	191	(14)
Further Classes of Pseudo-differential Operators Applicable to Modelling in Finance and Turbulence
Benjamin Jourdain and Tony Lelièvre	205	(19)
Mathematical Analysis of a Stochastic Differential Equation Arising in the Micro-Macro Modelling of Polymeric Fluids
Hannelore Lisei and Michael Scheutzow	224	(15)
On the Dispersion of Sets under the Action of an Isotropic Brownian Flow
Aubrey Truman, Chris N. Reynolds and David Williams	239	(24)
Stochastic Burgers Equation in d-dimensions - A One-dimensional Analysis: Hot and Cool Caustics and Intermittence of Stochastic Turbulence
Armen Shirikyan	263	(9)
A Version of the Law of Large Numbers and Applications
Manan Slodicka	272	(15)
Comprehensive Models for Wells
Enrique Thomann and Mina Ossiander	287	(11)
Stochastic Cascades Applied to the Navier-Stokes Equations
Aubrey Truman and Jiang-Lun Wu	298	(26)
Stochastic Burgers Equation with Lévy Space-Time White Noise
Tuskeng Zhang	324	(8)
A Comparison Theorem for Solutions of Backward Stochastic Differential Equations with Two Reflecting Barriers and Its Applications
Aubrey Truman and Huaizhong Zhao	332
Burgers Equation and the WKB-Langer Asymptotic L2 Approximation of Eigenfunctions and Their Derivatives