Global evolution of random vortex filament equation
Probability
2013-07-05 v5 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We prove the existence of a global solution for the filament equation with inital condition given by a geometric rough path in the sense of Lyons (1998).Our work gives a positive answer to a question left open in recent publications: Berselli and Gubinelli (2007) showed the existence of global solution for a smooth initial condition while Bessaih, Gubinelli, Russo (2005) proved the existence of a local solution for a general initial condition given by a rough path.
Keywords
Cite
@article{arxiv.1008.1086,
title = {Global evolution of random vortex filament equation},
author = {Z. Brzeźniak and M. Gubinelli and M. Neklyudov},
journal= {arXiv preprint arXiv:1008.1086},
year = {2013}
}
Comments
19 pages; minor revisions