Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability

Marc Arnaudon (1) , Ana Bela Cruzeiro (2)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 6086]
2 grupo de fisica matematica

We prove a variational principle for stochastic Lagrangian Navier-Stokes trajectories on manifolds. We study the behaviour of such trajectories concerning stability as well as rotation between particles; the two-dimensional torus case is described in detail.

Mots clés: stochastic analysis; diffusion processes; hydrodynamics

Domaines: Probabilités [math.PR]

Marc Arnaudon, Ana Bela Cruzeiro. Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability. Bulletin des Sciences Mathématiques, 2012, 8 (136), pp.857-881. ⟨10.1016/j.bulsci.2012.06.007⟩. ⟨hal-00472684⟩