The evolution of a random vortex filament
概率论
2007-05-23 v2 数学物理
math.MP
摘要
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.
引用
@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}
}
备注
25 pages, no figures, some additions, to appear in Ann. Probab