STOCHASTIC 1D BURGERS EQUATION AS A MODEL FOR HYDRODYNAMICAL TURBULENCE

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. © 2024 Independent University of Moscow.