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math.PR2013
Variational principle for weighted porous media equation
Alexandra Antoniouk, Marc Arnaudon
In this paper we state the variational principle for the weighted porous media equation. It extends V.I. Arnold's approach to the description of Euler flows as a geodesics on some…
math.PR2012★ 1 cited
Generalized Navier-Stokes flows and applications to incompressible viscous fluids
Alexandra Antoniouk, Marc Arnaudon, Ana Bela Cruzeiro
We introduce a notion of generalized stochastic flows on mani- folds, that extends to the viscous case the one defined by Brenier for perfect fluids. Their kinetic energy extends t…