Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An improved local wellposedness result for the modified KdV equation   The Cauchy problem for the modified KdV equation is shown to be locally well
posed for data u_0 in the space \hat(H^r_s) defined by the norm
||u_0||:=||<\xi>^s \hat(u_0)||_L^r', provided 4/3 < r \le 2, s \ge 1/2 -
1/(2r). For r=2 this coincides with the best possible result on the H^s - scale
due to Kenig, Ponce and Vega. The proof uses an appropriate variant of the
Fourier restriction norm method and linear as well as bilinear estimates for
the solutions of the Airy equation.

30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs