In my lectures I will present the principles of Kolmogorov's theory of turbulence, known as the K41 theory, in relation to its one-dimensional version, dealing with turbulence in the fictitious one-dimensional fluid. The latter is modeled by the stochastic Burgers equation, and the corresponding 1d versions of the laws of K41 theory are rigorously proved, based on the properties of solutions for that equation.
The lectures are based on my recent joint book A.Boritchev, S.Kuksin One-Dimensional Turbulence and the Stochastic Burgers Equation, AMS 2021.
12.7-12.21.pdf