Prépublication numéro 2004-19   du laboratoire LAGA, Université Paris 13

Hakima BESSAIH Massimiliano GUBINELLI Francesco RUSSO     The evolution of a random vortex filament   (format .ps compressé)

Résumé: We study an evolution problem in the space of continuous loops in three-dimensional Euclidean space modelled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting from Hölder regular loops with index greater than 1/3. When the Hölder regularity of the initial condition X is smaller or equal 1/2 we require X to be a "rough path" in the sense of Lyons. The solution will then live in an appropriate space of rough paths. In particular we can construct (local) solution starting from almost every Brownian loop.

Code(s) de Classification MSC2000:  60H05 Stochastic integrals ;  76B47 Vortex flows ; 

Mots Clés: Vortex filament, Rough path theory; Path-wise stochastic integration

Langue du texte: Anglais

Article reçu: 2004-07-08