Geodesic
Models of viscous fluids generated by martingales on the groups of diffeomorphisms
Journal of computational and engineering mathematics, Tome 10 (2023) no. 1, pp. 3-11.

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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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Yu. E. Gliklikh; D. S. Sergeeva. Models of viscous fluids generated by martingales on the groups of diffeomorphisms. Journal of computational and engineering mathematics, Tome 10 (2023) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/JCEM_2023_10_1_a0/