二维定常放热反应Euler方程熵解的存在性
Existence of Entropy Solutions to Two-Dimensional Steady Exothermically Reacting Euler Equations
摘要：
研究了理想气体在Arrhenius型动力学下进行一步放热化学反应的二维定常Euler方程组熵解的整体存在性.假设反应速率函数$ϕ(T)$具有正的下界。我们首先考虑Cauchy问题（即初值问题），即当来流为超音速时，寻找超音速下游反应流，并在初值的全变差足够小时建立熵解的整体存在性。然后，我们分析的问题，稳定的超音速，pharmically反应欧拉流通过Lipschitz楔，产生附加的爆震波连接到楔的顶点，然后可以制定为一个初边值问题。当楔形边界和来流的斜率的全变差适当小时，我们建立了包含附加爆轰波（弱或强，由楔形顶点处的楔形角决定）的熵解的全局存在性。同时也得到了整体解的下游渐近性态。
英文摘要：
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 $ϕ(T)$ 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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