Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global evolution of random vortex filament equation   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.

13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex