Z. Brzeźniak, M. Gubinelli and M. Neklyudov
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.
Z. Brzeźniak, M. Gubinelli and M. Neklyudov. Global evolution of random vortex filament equation. Papers of Massimiliano Gubinelli, 2010, version 5. https://mgubi.org/papers/paper/random-vortex-filament-evolution/
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