Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Travelling helices and the vortex filament conjecture in the
  incompressible Euler equations   We consider the Euler equations in ${\mathbb R}^3$ expressed in vorticity
form. A classical question that goes back to Helmholtz is to describe the
evolution of solutions with a high concentration around a curve. The work of Da
Rios in 1906 states that such a curve must evolve by the so-called binormal
curvature flow. Existence of true solutions concentrated near a given curve
that evolves by this law is a long-standing open question that has only been
answered for the special case of a circle travelling with constant speed along
its axis, the thin vortex-rings. We provide what appears to be the first
rigorous construction of {\em helical filaments}, associated to a
translating-rotating helix. The solution is defined at all times and does not
change form with time. The result generalizes to multiple similar helical
filaments travelling and rotating together.

0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg