Kolmogorov theory of turbulence and its rigorous model, given by the Burgers equation

I will present three main laws from the Kolmogorov theory of turbulence ("the K41 model"), discuss their versions for one-dimensional fluid and will show that the latter may be rigorously justified for the 1d fluid, described by the Burgers equation, via a qualitative analysis of the dynamical system which the equation defines in Sobolev spaces. The talk is based on a MS of my joint book with Alex Boritchev.