On rigorous 1d versions of the laws of Kolmogorov’s theory of turbulence
Vortrag von Prof. Dr. Sergei Kuksin
Datum: 04.12.24 Zeit: 17.15 - 18.45 Raum: ETH HG G 43
In his celebrated theory of turbulence, created in 1941 and known as the K41 theory, A.N.Kolmogorov considered the velocity u(t,x) of a turbulent flow of fluid. Assuming that the Reynolds number of the flow is large, he studied the increments u(t,x+r)-u(t,x) of u and heuristically examined their statistical properties, summarised in a number of law of the K41 theory. I will talk about fictitious 1d fluid, described by the stochastic Burgers equation, consider increments of its velocity field and will rigorously derive for them analogies of the corresponding laws from Kolmogorov's theory, strikingly close to these laws.