Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasilinear Schr\"odinger Equations   In this paper we prove local well-posedness for Quasi-linear Scrh\"odinger
equations with initial data in unweighted Sobolev Spaces. For small initial
data with minimal smoothness this has addressed by J. Marzuola, J. Metcalfe and
D. Tataru. This work does not attempt to address the minimal regularity for
initial data, but instead builds on the previous results of C. Kenig, G. Ponce,
and L. Vega to remove the smallness condition in unweighted spaces. This is
accomplished by developing a uncentered version of Doi's Lemma, which allows
one to prove Kato type smoothing estimates. These estimates make it possible to
achieve the necessary a priori linear results.

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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph