Burgers turbulence and dynamical systems

R. Iturriaga; K. Khanin

Burgers turbulence and dynamical systems

R. Iturriaga
, K. Khanin

Research output: Contribution to journal › Literature review › peer-review

Abstract

We discuss a dynamical system approach to a problem of Burgers turbulence. It is shown that there exists a unique stationary distribution for solutions to spatially periodic inviscid random forced Burgers equation in arbitrary dimension. The construction is based on analysis of minimizing orbits for time-dependent random Lagrangians on a d-dimensional torus. We also discuss how dynamical properties of minimizing trajectories lead to quantitative predictions for physically important universal critical exponents.

Original language	English
Journal	HP Laboratories Technical Report
Volume	BRIMS
Issue number	25
Publication status	Published - 18 Dec 2000

Keywords

Hamilton-jacobi equation
Random
Random burgers equation
Uniqueness of global minimizers

Cite this

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title = "Burgers turbulence and dynamical systems",

abstract = "We discuss a dynamical system approach to a problem of Burgers turbulence. It is shown that there exists a unique stationary distribution for solutions to spatially periodic inviscid random forced Burgers equation in arbitrary dimension. The construction is based on analysis of minimizing orbits for time-dependent random Lagrangians on a d-dimensional torus. We also discuss how dynamical properties of minimizing trajectories lead to quantitative predictions for physically important universal critical exponents.",

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TY - JOUR

T1 - Burgers turbulence and dynamical systems

AU - Iturriaga, R.

AU - Khanin, K.

PY - 2000/12/18

Y1 - 2000/12/18

N2 - We discuss a dynamical system approach to a problem of Burgers turbulence. It is shown that there exists a unique stationary distribution for solutions to spatially periodic inviscid random forced Burgers equation in arbitrary dimension. The construction is based on analysis of minimizing orbits for time-dependent random Lagrangians on a d-dimensional torus. We also discuss how dynamical properties of minimizing trajectories lead to quantitative predictions for physically important universal critical exponents.

AB - We discuss a dynamical system approach to a problem of Burgers turbulence. It is shown that there exists a unique stationary distribution for solutions to spatially periodic inviscid random forced Burgers equation in arbitrary dimension. The construction is based on analysis of minimizing orbits for time-dependent random Lagrangians on a d-dimensional torus. We also discuss how dynamical properties of minimizing trajectories lead to quantitative predictions for physically important universal critical exponents.

KW - Hamilton-jacobi equation

KW - Random

KW - Random burgers equation

KW - Uniqueness of global minimizers

UR - https://www.scopus.com/pages/publications/84862445944

M3 - Literature review

VL - BRIMS

JO - HP Laboratories Technical Report

JF - HP Laboratories Technical Report

IS - 25

ER -

Burgers turbulence and dynamical systems

Abstract

Keywords

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