Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On an Elliptic Free Boundary Problem and Subsonic Jet Flows for a Given
  Surrounding Pressure   This paper concerns compressible subsonic jet flows for a given surrounding
pressure from a two-dimensional finitely long convergent nozzle with straight
solid wall, which are governed by a free boundary problem for a quasilinear
elliptic equation. For a given surrounding pressure and a given incoming mass
flux, we seek a subsonic jet flow with the given incoming mass flux such that
the flow velocity at the inlet is along the normal direction, the flow
satisfies the slip condition at the wall, and the pressure of the flow at the
free boundary coincides with the given surrounding pressure. In general, the
free boundary contains two parts: one is the particle path connected with the
wall and the other is a level set of the velocity potential. We identify a
suitable space of flows in terms of the minimal speed and the maximal velocity
potential difference for the well-posedness of the problem. It is shown that
there is an optimal interval such that there exists a unique subsonic jet flow
in the space iff the length of the nozzle belongs to this interval.
Furthermore, the optimal regularity and other properties of the flows are
shown.

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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph