Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local well-posedness for the modified KdV equation in almost critical
  ^H^r_s-spaces   We study the Cauchy problem for the modified KdV equation for data u_0 in the
space ^H^r_s defined by the norm ||u_0||_{^H^r_s}:=||<\xi>^s u^_0||_{L^r'_\xi}.
Local well-posedness of this problem is established in the parameter range
2>=r>1, s>=1/2-1/2r, so the case (s,r)=(0,1), which is critical in view of
scaling considerations is almost reached. To show this result, we use an
appropriate variant of the Fourier restriction norm method as well as bi- and
trilinear estimates for solutions of the Airy equation.

27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph