MODELS OF VISCOUS FLUIDS GENERATED BY MARTINGALES ON THE GROUPS OF DIFFEOMORPHISMS

Abstract

We study two martingales on the group of Sobolev diffeomorphisms of the flat $n$-dimensional torus, they both are described by systems of two special equations with mean derivatives. The first one describes a solution of the Burgers equation on the torus that also satisfies an analog of continuity equation. The second martingale describes a certain non-Newtonian fluid on the torus that satisfies some special analogs of the Burgers equation and the continuity equation.