Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of Entropy Solutions to Two-Dimensional Steady Exothermically
  Reacting Euler Equations   We are concerned with the global existence of entropy solutions of the
two-dimensional steady Euler equations for an ideal gas, which undergoes a
one-step exothermic chemical reaction under the Arrhenius-type kinetics. The
reaction rate function $\phi(T)$ is assumed to have a positive lower bound. We
first consider the Cauchy problem (the initial value problem), that is, seek a
supersonic downstream reacting flow when the incoming flow is supersonic, and
establish the global existence of entropy solutions when the total variation of
the initial data is sufficiently small. Then we analyze the problem of steady
supersonic, exothermically reacting Euler flow past a Lipschitz wedge,
generating an additional detonation wave attached to the wedge vertex, which
can be then formulated as an initial-boundary value problem. We establish the
globally existence of entropy solutions containing the additional detonation
wave (weak or strong, determined by the wedge angle at the wedge vertex) when
the total variation of both the slope of the wedge boundary and the incoming
flow is suitably small. The downstream asymptotic behavior of the global
solutions is also obtained.

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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys