Moscow Mathematical Journal

Volume 24, Issue 4, October–December 2024 pp. 603–640.

Stochastic 1d Burgers Equation as a Model for Hydrodynamical Turbulence

Authors: Sergei Kuksin (1)
Author institution:(1) Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013 Paris, France;
Peoples' Friendship University of Russia, Moscow, Russia;
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia;
Institute for Financial Studies, Shandong University, Jinan, China.

Summary:

This work is a review with proofs of a group of results on the stochastic Burgers equation with small viscosity, obtained during the last two decades. These results jointly show that the equation makes a surprisingly good model of hydrodynamical turbulence. The model provides natural and rigorously justified analogies of a number of key predictions of the theory of turbulence, including the main assertions of the Kolmogorov approach to turbulence, known as the K41 theory.

2020 Math. Subj. Class. 35R60, 60H15, 76F02.

Keywords: Turbulence, Burgers equation, K41 theory, inner scale, structure function, inviscid limit.

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