Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Sharp Bilinear Estimate for the Bourgain-type Space with Application
  to the Benjamin Equation   This note shows the existence of a sharp bilinear estimate for the
Bourgain-type space and gives its application to the optimal local
well/ill-posedness of the Cauchy problem for the Benjamin equation.

8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat