Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness and scattering of 3D defocusing, cubic
  Schr\"odinger equation   In this paper, we study the global well-posedness and scattering of 3D
defocusing, cubic Schr\"odinger equation. Recently, Dodson [arXiv:2004.09618]
studied the global well-posedness in a critical Sobolev space
$\dot{W}^{11/7,7/6}$. In this paper, we aim to show that if the initial data
belongs to $\dot H^\frac12$ to guarantee the local existence, then some extra
weak space which is subcritical, is sufficient to prove the global
well-posedness. More precisely, we prove that if the initial data belongs to
$\dot{H}^{1/2}\cap \dot{W}^{s,1}$ for $12/13<s \leqslant 1$, then the
corresponding solution exists globally and scatters.

1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph