Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three Dimensional Steady Subsonic Euler Flows in Bounded Nozzles   In this paper, we study the existence and uniqueness of three dimensional
steady Euler flows in rectangular nozzles when prescribing normal component of
momentum at both the entrance and exit. If, in addition, the normal component
of the voriticity and the variation of Bernoulli's function at the exit are
both zero, then there exists a unique subsonic potential flow when the
magnitude of the normal component of the momentum is less than a critical
number. As the magnitude of the normal component of the momentum approaches the
critical number, the associated flows converge to a subsonic-sonic flow.
Furthermore, when the normal component of vorticity and the variation of
Bernoulli's function are both small, the existence of subsonic Euler flows is
established. The proof of these results is based on a new formulation for the
Euler system, a priori estimate for nonlinear elliptic equations with nonlinear
boundary conditions, detailed study for a linear div-curl system, and delicate
estimate for the transport equations.

17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat