Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous dependence for $H^{2}$ critical nonlinear Schr\"{o}dinger
  equations in high dimensions   The global existence of solutions in $H^{2}$ is well known for $H^{2}$
critical nonlinear Schr\"{o}dinger equations with small initial data in high
dimensions $d\geq8$. However, even though the solution is constructed by a
fixed-point technique, continuous dependence in $H^{2}$ does not follow from
the contraction mapping argument. Comparing with the low dimension cases
$4<d<8$, there is an obstruction to this approach because of the sub-quadratic
nature of the nonlinearity(which makes the derivative of the nonlinearity
non-Lipschitz). In this paper, we resolve this difficulty by applying exotic
Strichartz spaces of lower order instead and show that the solution depends
continuously on the initial value in the sense that the local flow is
continuous $H^{2}\rightarrow H^{2}$.

5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga