The evolution of a random vortex filament

Details The evolution of a random vortex filament The evolution of a random vortex filament

2004-07-08

arxiv.org/abs/math/0407141v2

Mathematics

Probability

25 pages, no figures, some additions, to appear in Ann. Probab

Scientific paper

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 H\"older regular loops with index greater than 1/3. When the H\"older 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.

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