Burgers turbulence and dynamical systems

R. Iturriaga, K. Khanin

Research output: Contribution to journalLiterature 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 languageEnglish
JournalHP Laboratories Technical Report
VolumeBRIMS
Issue number25
Publication statusPublished - 18 Dec 2000

Fingerprint

Burger equation
dynamical systems
turbulence
trajectories
exponents
orbits
predictions

Keywords

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

Cite this

Iturriaga, R., & Khanin, K. (2000). Burgers turbulence and dynamical systems. HP Laboratories Technical Report, BRIMS(25).
Iturriaga, R. ; Khanin, K. / Burgers turbulence and dynamical systems. In: HP Laboratories Technical Report. 2000 ; Vol. BRIMS, No. 25.
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Iturriaga, R & Khanin, K 2000, 'Burgers turbulence and dynamical systems', HP Laboratories Technical Report, vol. BRIMS, no. 25.

Burgers turbulence and dynamical systems. / Iturriaga, R.; Khanin, K.

In: HP Laboratories Technical Report, Vol. BRIMS, No. 25, 18.12.2000.

Research output: Contribution to journalLiterature review

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.

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KW - Random

KW - Random burgers equation

KW - Uniqueness of global minimizers

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M3 - Literature review

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Iturriaga R, Khanin K. Burgers turbulence and dynamical systems. HP Laboratories Technical Report. 2000 Dec 18;BRIMS(25).