Kolmogorov's theory of turbulence and its rigorous 1d model
Sergei Kuksin
TL;DR
This paper reviews a recent book on 1D turbulence modeled by the stochastic Burgers equation, connecting it to Kolmogorov's turbulence theory and highlighting recent rigorous mathematical developments.
Contribution
It synthesizes recent advances in the mathematical understanding of 1D turbulence through the stochastic Burgers equation, emphasizing rigorous results related to Kolmogorov's theory.
Findings
Rigorous mathematical results on 1D turbulence models
Connections between stochastic Burgers equation and Kolmogorov theory
Summary of recent developments in turbulence modeling
Abstract
This paper is a synopsis of the recent book A. Boritchev, S. Kuksin, \textit{One-Dimensional Turbulence and the Stochastic Burgers Equation}, AMS Publications, 2021 (to appear). The book is dedicated to the stochastic Burgers equation as a model for 1d turbulence, and the paper discusses its content in relation to the Kolmogorov theory of turbulence.
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Taxonomy
TopicsStochastic processes and financial applications · Navier-Stokes equation solutions · Differential Equations and Numerical Methods