Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cauchy problem of nonlinear Schr\"odinger equation with Cauchy problem
  of nonlinear Schr\"odinger equation with initial data in Sobolev space
  $W^{s,p}$ for $p<2$   In this paper, we consider in $R^n$ the Cauchy problem for nonlinear
Schr\"odinger equation with initial data in Sobolev space $W^{s,p}$ for $p<2$.
It is well known that this problem is ill posed. However, We show that after a
linear transformation by the linear semigroup the problem becomes locally well
posed in $W^{s,p}$ for $\frac{2n}{n+1}<p<2$ and $s>n(1-\frac{1}{p})$. Moreover,
we show that in one space dimension, the problem is locally well posed in $L^p$
for any $1<p<2$.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn