The evolution of a random vortex filament
Probability
2007-05-23 v2 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.math/0407141,
title = {The evolution of a random vortex filament},
author = {Hakima Bessaih and Massimiliano Gubinelli and Francesco Russo},
journal= {arXiv preprint arXiv:math/0407141},
year = {2007}
}
Comments
25 pages, no figures, some additions, to appear in Ann. Probab