Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness and stability for the Vlasov-Poisson system with spatial
  density in Orlicz spaces   In this paper, we establish uniqueness of the solution of the Vlasov-Poisson
system with spatial density belonging to a certain class of Orlicz spaces. This
extends the uniqueness result of Loeper (which holds for uniformly bounded
density) and the uniqueness result of the second author. Uniqueness is a direct
consequence of our main result, which provides a quantitative stability
estimate for the Wasserstein distance between two weak solutions with spatial
density in such Orlicz spaces, in the spirit of Dobrushin's proof of stability
for mean-field PDEs. Our proofs are built on the second-order structure of the
underlying characteristic system associated to the equation.

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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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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: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin