  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.
