Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on local theory for Schr\"odinger maps near harmonic maps   We consider the initial-value problem for the equivariant Schr\"odinger maps
near a family of harmonic maps. We provide some supplemental arguments for the
proof of local well-posedness result by Gustafson, Kang and Tsai in [Duke Math.
J. 145(3) 537--583, 2008]. We also prove that the solution near harmonic maps
is unique in $C(I;\dot{H}^1(\mathbb{R}^2)\cap\dot{H}^2(\mathbb{R}^2))$ for time
interval $I$. In the proof, we give a justification of the derivation of the
modified Schr\"odinger map equation in low regularity settings without
smallness of energy.

19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph