Stochastic Variational Principles for Dissipative Equations with Advected Quantities

We develop symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group, obtaining deterministic constrained variational principles and dissipative equations of motion in spatial representation. We discuss in detail the situation when the group in the general theory is a group of diffeomorphisms and derive, as an application, an MHD system for viscous compressible fluids.

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