Nonlinear Stochastic PDEs: Hydrodynamic Limit and Burgers' Turbulence

by Tadahisa Funaki (Editor), Wojbor Woyczynski (Editor)

Overview

This volume is a based on recent research which focuses on the area of nonlinear shastic partial differential equations. The first section contains work on fundamental problems of hydrodynamic limit for particle systems and on random media. The second part groups together papers under the umbrella of the name "Burgers' turbulence", although a broader spectrum of shastic problem for the Burgers' equation is actually addressed. Finally, the last part deals with the shastic Navier-Stokes equation both from mathematical and physical perspective. This book is suitable for mathematicians and students.

Product Details

ISBN-13:	9781461384700
Publisher:	Springer New York
Publication date:	11/30/2011
Series:	IMA Volumes in Mathematics and its Applications Series , #77
Edition description:	Softcover reprint of the original 1st ed. 1996
Pages:	312
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

I. Hydrodynamic Limit, Random Media, and Related Problems.- Hydrodynamic limit for lattice gas reversible under Bernoulli measures.- Equilibrium fluctuations of nongradient reversible particle systems.- The reversible measures of a conservative system with finite range interactions.- Diffusion in disordered media.- Reaction-diffusion equations in the random media: localization and intermittency.- Approximation of a one-dimensional shastic PDE by local mean field type lattice systems.- Sharp asymptotics of diffusion processes with small parameter and applications to metastable behavior.- II. Burgers’ Turbulence.- Intermediate asymptotics of statistical solutions of Burgers’ equation.- On a shastic PDE related to Burgers’ equation with noise.- Shock density in Burgers’ turbulence.- Model description of passive tracer density fields in the framework of Burgers’ and other related model equations.- Evaluation of spectral behavior for large ensembles of exact solutions to Burgers’ equation for Thomas initial conditions.- III. Shastic Navier-Stokes Equation.- Stationary solutions of two-dimensional Navier-Stokes equations with random perturbation.- Nonlinear filtering of shastic Navier-Stokes equation.- Mesoscopic modelling and shastic simulations of turbulent flows.- Algebraic energy spectra in shastic problems for the incompressible Navier-Stokes equation; relation to other nonlinear problems.