Stochastic geometric mechanics with diffeomorphisms

Darryl D. Holm, Erwin Luesink

Published 2021-08-17Version 1

Noether's celebrated theorem associating symmetry and conservation laws in classical field theory is adapted to allow for broken symmetry in geometric mechanics and is shown to play a central role in deriving and understanding the generation of fluid circulation via the Kelvin-Noether theorem for ideal fluids with stochastic advection by Lie transport (SALT).