Bessaih, HakimaGubinelli, M.Russo, F.2024-02-082024-02-082005-09-01https://wyoscholar.uwyo.edu/handle/internal/1699https://doi.org/10.15786/wyoscholar/9774We 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.enghttps://creativecommons.org/licenses/by/4.0/vortex filamentsrough path theorypath-wise stochastic integrationMathematicsjournal contribution10.1214/009117905000000323