Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the instability for the cubic nonlinear Schrodinger equation   We study the flow map associated to the cubic Schrodinger equation in space
dimension at least three. We consider initial data of arbitrary size in $H^s$,
where $0<s<s_c$, $s_c$ the critical index, and perturbations in $H^\si$, where
$\si<s_c$ is independent of $s$. We show an instability mechanism in some
Sobolev spaces of order smaller than $s$. The analysis relies on two features
of super-critical geometric optics: creation of oscillation, and ghost effect.

27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th