Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bounds for parabolic equations and the Landau equation   We consider a parabolic equation in nondivergence form, defined in the full
space $[0,\infty) \times \mathbb R^d$, with a power nonlinearity as the right
hand side. We obtain an upper bound for the solution in terms of a weighted
control in $L^p$. This upper bound is applied to the homogeneous Landau
equation with moderately soft potentials. We obtain an estimate in
$L^\infty(\mathbb R^d)$ for the solution of the Landau equation, for positive
time, which depends only on the mass, energy and entropy of the initial data.

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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg