Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a 1D nonlocal transport equation with nonlocal velocity and
  subcritical or supercritical diffusion   We study a 1D transport equation with nonlocal velocity with subcritical or
supercritical dissipation. For all data in the weighted Sobolev space
$H^{k}(w_{\lambda,\kappa}) \cap L^{\infty},$ with $k=\max(0,3/2-\alpha)$ and
$w_{\lambda, \kappa}$ is a given family of Muckenhoupt weights. We prove a
global existence result in the subcritical case $\alpha \in (1,2)$. We also
prove a local existence theorem for large data in $H^{2}(w_{\lambda,
\kappa})\cap L^{\infty}$ in the supercritical case $\alpha \in (0,1)$. The
proofs are based on the use of the weighted Littlewood-Paley theory,
interpolation along with some new commutator estimates.

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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con