Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasilinear Schr\"odinger equations I: Small data and quadratic
  interactions   In this article we prove local well-posedness in low-regularity Sobolev
spaces for general quasilinear Schr\"odinger equations. These results represent
improvements of the pioneering works by Kenig-Ponce-Vega and
Kenig-Ponce-Rolvung-Vega, where viscosity methods were used to prove existence
of solutions in very high regularity spaces. Our arguments here are purely
dispersive. The function spaces in which we show existence are constructed in
ways motivated by the results of Mizohata, Ichinose, Doi, and others, including
the authors.

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The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
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The categories of this paper are: stat
30
The categories of this paper are: q-alg
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph