数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (1): 1-38.doi: 10.1016/S0252-9602(13)60123-X
• 论文 • 下一篇
陈贵强1,2|肖长国2|张永前2
CHEN Gui-Qang1,2, XIAO Chang-Guo2, ZHANG Yong-Qian2
摘要:
We are concerned with the global existence of entropy solutions of the twodimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function (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 global 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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