Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness for 2D radial Schr\"odinger maps into the sphere   We prove global well-posedness for a cubic, non-local Schr\"odinger equation
with radially-symmetric initial data in the critical space $L^2(\R^2)$, using
the framework of Kenig-Merle and Killip-Tao-Visan. As a consequence, we obtain
a global well-posedness result for Schr\"odinger maps from $\R^2$ into $\S^2$
(Landau-Lifshitz equation) with radially symmetric initial data (with no size
restriction).

29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an