Non-Newtonian fluids and stochastic analysis on the groups of diffeomorphisms

Abstract

In the framework of Lagrangian approach to hydrodynamics, we suggest a special stochastic perturbation of the flows of perfect fluids on flat n-dimensional torus and obtain the description of viscous fluids with viscous term in the form of some second-order differential operator more general than Laplacian that may depend on time. A particular case is the viscous fluids with time-dependent viscosity.

Keywords:

• group of diffeomorphisms
• flat torus
• stochastic perturbation
• non-Newtonian fluids

AMS Subject Classifications:

• 58J65
• 60H30
• 76D05
• 76D09
• 76M35