Models of Viscous Fluids Generated by Martingales on the Groups of Diffeomorphisms
Copyright policy )Models of Viscous Fluids Generated by Martingales on the Groups of Diffeomorphisms
Summary: 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.
- Voronezh State University Russian Federation
mean derivatives, Diffusion processes and stochastic analysis on manifolds, flat torus, viscous hydrodynamics, Navier-Stokes equations for incompressible viscous fluids, Applications of stochastic analysis (to PDEs, etc.), groups of diffeomorphisms
mean derivatives, Diffusion processes and stochastic analysis on manifolds, flat torus, viscous hydrodynamics, Navier-Stokes equations for incompressible viscous fluids, Applications of stochastic analysis (to PDEs, etc.), groups of diffeomorphisms
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