Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic nonlinear Schr\"odinger equation in critical $H^s(\T^n)$ spaces   In this paper we prove some multi-linear Strichartz estimates for solutions
to the linear Schr\"odinger equations on torus $\T^n$. Then we apply it to get
some local well-posed results for nonlinear Schr\"odinger equation in critical
$H^{s}(\T^n)$ spaces. As by-products, the energy critical global well-posed
results and energy subcritical global well-posed results with small initial
data are also obtained.

23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org