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Evolution of a Random Vortex Filament, The

Bessaih, Hakima
Gubinelli, M.
Russo, F.
Abstract
Description
We study an evolution problem in the space of continuous loops in a three-dimensional Euclidean space modeled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting from Holder regular loops with index greater than 1/3. When the Holder regularity of the initial condition X is smaller or equal to 1/2, we require X to be a rough path in the sense of Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310, System Control and Rough Paths (2002). Oxford Univ. Press]. 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.
Date
2005-09-01
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University of Wyoming. Libraries
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Keywords
vortex filaments , rough path theory , path-wise stochastic integration , Mathematics
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