What is it about?
This is a review of a group of results which jointly show that the stochastic Burgers equation makes a 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.
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Why is it important?
This is for the first time when a hydrodynamical model, given by a nonlinear partial differential equation, allowed to prove rigorously results that make natural analogies of all predictions of the Kolmogorov theory of turbulence as well as of some other basic assertions from hydrodynamical turbulence.
Perspectives
It was a great surprise to realise that a model, given by a relatively simple partial differential equation with one space variable, makes a precise and rigorous model of the extremely complicated phenomenon of turbulence.
Sergei Kuksin
Universite Paris Diderot
Read the Original
This page is a summary of: The K41 theory and turbulence in 1D Burgers equation, Chaos An Interdisciplinary Journal of Nonlinear Science, February 2024, American Institute of Physics,
DOI: 10.1063/5.0177259.
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