Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transonic Shocks In Multidimensional Divergent Nozzles   We establish existence, uniqueness and stability of transonic shocks for
steady compressible non-isentropic potential flow system in a multidimensional
divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit
pressure. The proof is based on solving a free boundary problem for a system of
partial differential equations consisting of an elliptic equation and a
transport equation. In the process, we obtain unique solvability for a class of
transport equations with velocity fields of weak regularity(non-Lipschitz), an
infinite dimensional weak implicit mapping theorem which does not require
continuous Frechet differentiability, and regularity theory for a class of
elliptic partial differential equations with discontinuous oblique boundary
conditions.

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The categories of this paper are: econ
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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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: solv-int
1
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: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom