The evolution of a random vortex filament

Hakima Bessaih, Massimiliano Gubinelli and Francesco Russo

First issued 8 July 2004 · PDF

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 Hölder regular loops with index greater than 1/3. When the Hölder 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.

Versions

1. Version 2 (arXiv v2) current
   2 December 2004
   arXiv comments: 25 pages, no figures, some additions, to appear in Ann. Probab
   PDF · LaTeX source · files and digests · arXiv:math/0407141
2. Version 1 (arXiv v1)
   8 July 2004
   arXiv comments: 25 pages, no figures
   PDF · LaTeX source · files and digests · arXiv:math/0407141

Cite

Hakima Bessaih, Massimiliano Gubinelli and Francesco Russo. The evolution of a random vortex filament. Papers of Massimiliano Gubinelli, 2004, version 2. https://mgubi.org/papers/paper/random-vortex-filament/

Licence: arXiv.org non-exclusive license to distribute, assumed for submissions of 1991-2003; all other rights reserved to the authors

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