Ebook: Nonlinear Stochastic PDEs: Hydrodynamic Limit and Burgers’ Turbulence

This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is based on the proceedings of the period of concentration on Stochas­ tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "Emerging Applications of Probability." We thank Tadahisa Funaki and Wojbor A. Woyczynski for organizing this meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE A workshop on Nonlinear Stochastic Partial Differential Equations was held during the week of March 21 at the Institute for Mathematics and Its Applications at the University of Minnesota. It was part of the Special Year on Emerging Applications of Probability program put together by an organizing committee chaired by J. Michael Steele. The selection of topics reflected personal interests of the organizers with two areas of emphasis: the hydrodynamic limit problems and Burgers' turbulence and related models. The talks and the papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.

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This volume is a based on recent research which focuses on the area of nonlinear stochastic 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 stochastic problem for the Burgers' equation is actually addressed. Finally, the last part deals with the stochastic Navier-Stokes equation both from mathematical and physical perspective. This book is suitable for mathematicians and students.

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This volume is a based on recent research which focuses on the area of nonlinear stochastic 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 stochastic problem for the Burgers' equation is actually addressed. Finally, the last part deals with the stochastic Navier-Stokes equation both from mathematical and physical perspective. This book is suitable for mathematicians and students.
Content:
Front Matter....Pages i-xviii
Hydrodynamic Limit for Lattice Gas Reversible under Bernoulli Measures....Pages 1-40
Equilibrium Fluctuations of Nongradient Reversible Particle Systems....Pages 41-51
The Reversible Measures of a Conservative System with Finite Range Interactions....Pages 53-64
Diffusion in Disordered Media....Pages 65-79
Reaction-Diffusion Equations in the Random Media: Localization and Intermittency....Pages 81-109
Approximation of a One-Dimensional Stochastic PDE by Local Mean Field Type Lattice Systems....Pages 111-125
Sharp Asymptotics of Diffusion Processes with Small Parameter and Applications to Metastable Behavior....Pages 127-136
Intermediate Asymptotics of Statistical Solutions of Burgers’ Equation....Pages 137-146
On a Stochastic PDE Related to Burgers’ Equation with Noise....Pages 147-156
Shock Density in Burgers’ Turbulence....Pages 157-165
Model Description of Passive Tracer Density Fields in the Framework of Burgers’ and Other Related Model Equations....Pages 167-191
Evaluation of Spectral Behavior for Large Ensembles of Exact Solutions to Burgers’ Equation for Thomas Initial Conditions....Pages 193-235
Stationary Solutions of Two-Dimensional Navier-Stokes Equations with Random Perturbation....Pages 237-245
Nonlinear Filtering of Stochastic Navier-Stokes Equation....Pages 247-260
Mesoscopic Modelling and Stochastic Simulations of Turbulent Flows....Pages 261-291
Algebraic Energy Spectra in Stochastic Problems for the Incompressible Navier-Stokes Equation; Relation to Other Nonlinear Problems....Pages 293-312

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This volume is a based on recent research which focuses on the area of nonlinear stochastic 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 stochastic problem for the Burgers' equation is actually addressed. Finally, the last part deals with the stochastic Navier-Stokes equation both from mathematical and physical perspective. This book is suitable for mathematicians and students.
Content:
Front Matter....Pages i-xviii
Hydrodynamic Limit for Lattice Gas Reversible under Bernoulli Measures....Pages 1-40
Equilibrium Fluctuations of Nongradient Reversible Particle Systems....Pages 41-51
The Reversible Measures of a Conservative System with Finite Range Interactions....Pages 53-64
Diffusion in Disordered Media....Pages 65-79
Reaction-Diffusion Equations in the Random Media: Localization and Intermittency....Pages 81-109
Approximation of a One-Dimensional Stochastic PDE by Local Mean Field Type Lattice Systems....Pages 111-125
Sharp Asymptotics of Diffusion Processes with Small Parameter and Applications to Metastable Behavior....Pages 127-136
Intermediate Asymptotics of Statistical Solutions of Burgers’ Equation....Pages 137-146
On a Stochastic PDE Related to Burgers’ Equation with Noise....Pages 147-156
Shock Density in Burgers’ Turbulence....Pages 157-165
Model Description of Passive Tracer Density Fields in the Framework of Burgers’ and Other Related Model Equations....Pages 167-191
Evaluation of Spectral Behavior for Large Ensembles of Exact Solutions to Burgers’ Equation for Thomas Initial Conditions....Pages 193-235
Stationary Solutions of Two-Dimensional Navier-Stokes Equations with Random Perturbation....Pages 237-245
Nonlinear Filtering of Stochastic Navier-Stokes Equation....Pages 247-260
Mesoscopic Modelling and Stochastic Simulations of Turbulent Flows....Pages 261-291
Algebraic Energy Spectra in Stochastic Problems for the Incompressible Navier-Stokes Equation; Relation to Other Nonlinear Problems....Pages 293-312
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