Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and Optimal Convergence Rates of Multi-dimensional Subsonic
  Potential Flows Through an Infinitely Long Nozzle with an Obstacle Inside   In this paper, the well-posedness and optimal convergence rates of subsonic
irrotational flows through a three dimensional infinitely long nozzle with a
smooth obstacle inside are established. More precisely, the global existence
and uniqueness of the uniformly subsonic flow are obtained via variational
formulation as long as the incoming mass flux is less than a critical value.
Furthermore, with the aid of delicate choice of weight functions, we prove the
optimal convergence rates of the flow at far fields via weighted energy
estimates and Nash-Moser iteration.

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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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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: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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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: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: econ