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math-ph2019★ 16 cited
Lagrangian averaged stochastic advection by Lie transport for fluids
Theodore D. Drivas, Darryl D. Holm, James-Michael Leahy
We formulate a class of stochastic partial differential equations based on Kelvin's circulation theorem for ideal fluids. In these models, the velocity field is randomly transporte…
math.PR2019
On a rough perturbation of the Navier-Stokes system and its vorticity formulation
Martina Hofmanova, James-Michael Leahy, Torstein Nilssen
We introduce a rough perturbation of the Navier-Stokes system and justify its physical relevance from balance of momentum and conservation of circulation in the inviscid limit. We…