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Abstract: We prove the existence of a global solution for the filament equation withinital condition given by a geometric rough path in the sense of Lyons1998.Our work gives a positive answer to a question left open in recentpublications: Berselli and Gubinelli 2007 showed the existence of globalsolution for a smooth initial condition while Bessaih, Gubinelli, Russo 2005proved the existence of a local solution for a general initial condition givenby a rough path.



Author: Z. Brze┼║niak, M. Gubinelli, M. Neklyudov

Source: https://arxiv.org/







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