One-Dimensional Turbulence and the Stochastic Burgers Equation

2/3-law, and the Kolmogorov–Obukhov law.

The first part of the book deals with the stochastic Burgers equation, including the inviscid limit for the equation, its asymptotic in time behavior, and a theory of generalised L

1

L1-solutions. This section makes a self-consistent introduction to stochastic PDEs. The relative simplicity of the model allows us to present in a light form many of the main ideas from the general theory of this field. The second part, dedicated to the relation of one-dimensional turbulence with the K41 theory, could serve for a mathematical reader as a rigorous introduction to the literature on hydrodynamical turbulence, all of which is written on a physical level of rigor.