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

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

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (1): 1-38.doi: 10.1016/S0252-9602(13)60123-X

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

陈贵强^1,2|肖长国²|张永前²

1. Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK；
2. School of Mathematical Sciences, Fudan University, Shanghai 200433, China；

收稿日期:2013-05-10 修回日期:2013-10-19 出版日期:2014-01-20 发布日期:2014-01-20
基金资助:
The research of Gui-Qiang CHEN was supported in part by the UK EPSRC Science and Innovation Award to the Oxford Centre for Nonlinear PDE (EP/E035027/1), the NSFC under a joint project Grant 10728101, and the Royal Society-Wolfson Research Merit Award (UK). Changguo XIAO was supported in part by the NSFC under a joint project Grant 10728101. Yongqian ZHANG was supported in part by NSFC Project 11031001, NSFC Project 11121101, and the 111 Project B08018 (China).

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

CHEN Gui-Qang^1,2, XIAO Chang-Guo², ZHANG Yong-Qian²

1. Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK；
2. School of Mathematical Sciences, Fudan University, Shanghai 200433, China；

Received:2013-05-10 Revised:2013-10-19 Online:2014-01-20 Published:2014-01-20
Supported by:
The research of Gui-Qiang CHEN was supported in part by the UK EPSRC Science and Innovation Award to the Oxford Centre for Nonlinear PDE (EP/E035027/1), the NSFC under a joint project Grant 10728101, and the Royal Society-Wolfson Research Merit Award (UK). Changguo XIAO was supported in part by the NSFC under a joint project Grant 10728101. Yongqian ZHANG was supported in part by NSFC Project 11031001, NSFC Project 11121101, and the 111 Project B08018 (China).

摘要/Abstract

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.

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

Abstract:

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

中图分类号:

35L65

陈贵强, 肖长国, 张永前. EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS[J]. 数学物理学报(英文版), 2014, 34(1): 1-38.

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

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

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