Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness for the fifth-order KdV equation in
  $H^{-1}(\mathbb{R})$   We prove global well-posedness of the fifth-order Korteweg-de Vries equation
on the real line for initial data in $H^{-1}(\mathbb{R})$. By comparison, the
optimal regularity for well-posedness on the torus is known to be
$L^2(\mathbb{R}/\mathbb{Z})$.
  In order to prove this result, we develop a strategy for integrating the
local smoothing effect into the method of commuting flows introduced previously
in the context of KdV. It is this synthesis that allows us to go beyond the
known threshold on the torus.

24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
1
The categories of this paper are: cs
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg