Mathematics – Probability
Scientific paper
2004-07-08
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.
Bessaih Hakima
Gubinelli Massimiliano
Russo Francesco
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