Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low regularity local well-posedness of the Derivative Nonlinear
  Schr\"odinger Equation with periodic initial data   The Cauchy problem for the derivative nonlinear Schr\"odinger equation with
periodic boundary condition is considered. Local well-posedness for periodic
initial data u_0 in the space ^H^s_r, defined by the norms
||u_0||_{^H^s_r}=||<xi>^s ^u_0||_{l^r'} is shown in the parameter range s>=
1/2, 2>r>4/3. The proof is based on an adaptation of the gauge transform to the
periodic setting and an appropriate variant of the Fourier restriction norm
method.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs