Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local well-posedness of the Boltzmann equation with polynomially
  decaying initial data   We consider the Cauchy problem for the spatially inhomogeneous non-cutoff
Boltzmann equation with polynomially decaying initial data in the velocity
variable. We establish short-time existence for any initial data with this
decay in a fifth order Sobolev space by working in a mixed $L^2$ and $L^\infty$
space that allows to compensate for potential moment generation and obtaining
new estimates on the collision operator that are well-adapted to this space.
Our results improve the range of parameters for which the Boltzmann equation is
well-posed in this decay regime, as well as relax the restrictions on the
initial regularity. As an application, we can combine our existence result with
the recent conditional regularity estimates of Imbert-Silvestre
(arXiv:1909.12729 [math.AP]) to conclude solutions can be continued for as long
as the mass, energy, and entropy densities remain under control. This
continuation criterion was previously only available in the restricted range of
parameters of previous well-posedness results for polynomially decaying initial
data.

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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn