Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaling limit of Modulation Spaces and Their Applications   Modulation spaces $M^s_{p,q}$ were introduced by Feichtinger \cite{Fei83} in
1983. By resorting to the wavelet basis, B\'{e}nyi and Oh \cite{BeOh20} defined
a modified version to Feichtinger's modulation spaces for which the symmetry
scalings are emphasized for its possible applications in PDE. By carefully
investigating the scaling properties of modulation spaces and their connections
with the wavelet basis, we will introduce a class of generalized modulation
spaces, which contain both Feichtinger's and B\'{e}nyi and Oh's modulation
spaces. As their applications, we will give a local well-posedness and a (small
data) global well-posedness results for NLS in some rougher generalized
modulation spaces, which generalize the well posedness results of \cite{BeOk09}
and \cite{WaHud07}, and certain super-critical initial data in $H^s$ or in
$L^p$ are involved in these spaces.

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The categories of this paper are: eess
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat