Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal form approach to the one-dimensional periodic cubic nonlinear
  Schr\"odinger equation in almost critical Fourier-Lebesgue spaces   In this paper, we study the one-dimensional cubic nonlinear Schr\"odinger
equation (NLS) on the circle. In particular, we develop a normal form approach
to study NLS in almost critical Fourier-Lebesgue spaces. By applying an
infinite iteration of normal form reductions introduced by the first author
with Z. Guo and S. Kwon (2013), we derive a normal form equation which is
equivalent to the renormalized cubic NLS for regular solutions. For rough
functions, the normal form equation behaves better than the renormalized cubic
NLS, thus providing a further renormalization of the cubic NLS. We then prove
that this normal form equation is unconditionally globally well-posed in the
Fourier-Lebesgue spaces $\mathcal{F} L^p(\mathbb{T})$, $1 \leq p < \infty$. By
inverting the transformation, we conclude global well-posedness of the
renormalized cubic NLS in almost critical Fourier-Lebesgue spaces in a suitable
sense. This approach also allows us to prove unconditional uniqueness of the
(renormalized) cubic NLS in $\mathcal{F} L^p(\mathbb{T})$ for $1\leq p \leq
\frac32$.

9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol