EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

doi:10.1016/S0252-9602(13)60123-X

Abstract

Abstract:

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.

Key words: combustion, detonation wave, stability, Glimm scheme, fractional-step, supersonic flow, reacting Euler flow, Riemann problem, entropy solutions, two-dimensional, steady flow, asymptotic behavior

CLC Number:

35L65

CHEN Gui-Qang, XIAO Chang-Guo, ZHANG Yong-Qian. EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS[J].Acta mathematica scientia,Series B, 2014, 34(1): 1-38.

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