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

Yu. E. Gliklikh, D. S. Sergeeva

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.


Keywords


mean derivatives; flat torus; groups of diffeomoirphisms; viscous hydrodynamics.

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References


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