Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large global solutions for nonlinear Schr\"odinger equations I,
  mass-subcritical cases   In this paper, we consider the nonlinear Schr\"odinger equation, $$
  i\partial_{t}u+\Delta u= \mu|u|^p u, \quad (t,x)\in \mathbb{R}^{d+1}, $$ with
$\mu=\pm1, p>0$.
  In this work, we consider the mass-subcritical cases, that is, $p\in
(0,\frac4d)$. We prove that under some restrictions on $d,p$, any radial
initial data in the critical space $\dot H^{s_c}(\mathbb{R}^d)$ with compact
support, implies global well-posedness.

21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an