Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An improved local well-posedness result for the one-dimensional Zakharov
  system   The 1D Cauchy problem for the Zakharov system is shown to be locally
well-posed for low regularity Schr\"odinger data u_0 \in \hat{H^{k,p}} and wave
data (n_0,n_1) \in \hat{H^{l,p}} \times \hat{H^{l-1,p}} under certain
assumptions on the parameters k,l and 1<p\le 2, where \|u_0\|_{\hat{H^{k,p}}}
:= \| < \xi >^k \hat{u_0}\|_{L^{p'}}, generalizing the results for p=2 by
Ginibre, Tsutsumi, and Velo. Especially we are able to improve the results from
the scaling point of view, and also allow suitable k<0, l<-1/2, i.e. data u_0
\not\in L^2 and (n_0,n_1)\not\in H^{-1/2}\times H^{-3/2}, which was excluded in
the case p=2.

29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat