Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous Dependence of Cauchy Problem For Nonlinear Schr\"{o}dinger
  Equation in $H^{s}$   We consider the Cauchy problem for the nonlinear Schr\"{o}dinger equation $i
\partial_{t}u+ \Delta u=\lambda_{0}u+\lambda_{1}|u|^\alpha u$ in
$\mathbb{R}^{N}$, where $\lambda_{0},\lambda_{1}\in\mathbb{C}$, in $H^s$
subcritical and critical case: $0<\alpha\leq\frac{4}{N-2s}$ when
$1<s<\frac{N}{2}$ and $0<\alpha<+\infty$ when $s\geq\frac{N}{2}$. We show that
the solution depends continuously on the initial value in the standard sense in
$H^{s}(\mathbb{R}^{N})$ if $\alpha$ satisfies certain assumptions.

17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg