  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.
