University of Wyoming
Browse
FACW_MATH_2005_2168894X_Bessaih_Gubinelli_Russo.pdf (267.94 kB)

Evolution of a Random Vortex Filament, The

Download (267.94 kB)
journal contribution
posted on 2021-11-15, 21:40 authored by Hakima Bessaih, M. Gubinelli, F. Russo
We study an evolution problem in the space of continuous loops in a three-dimensional Euclidean space modeled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local solution starting from Holder regular loops with index greater than 1/3. When the Holder regularity of the initial condition X is smaller or equal to 1/2, we require X to be a rough path in the sense of Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310, System Control and Rough Paths (2002). Oxford Univ. Press]. 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.

History

ISO

eng

Language

English

Publisher

University of Wyoming. Libraries

Journal title

Annals of Probability

Collection

Faculty Publication - Department of Mathmatics & Statistics

Department

  • Library Sciences - LIBS

Usage metrics

    Department of Mathematics and Statistics

    Licence

    Exports