On the stochastic Burgers equation with some applications to turbulence and astrophysics

We summarise a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces and relating these results to a discussion of stochastic turbulence. We show that for small viscosities there exists a vortex filament structure near to the Maxwell set. We discuss how this vorticity is directly related to the adhesion model for the evolution of the early universe and include new explicit formulas for the distribution of mass within the shock.