On transonic shocks in a conic divergent nozzle with axi-symmetric exit pressures |
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Authors: | Jun Li Zhouping Xin |
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Institution: | a Department of Mathematics & IMS, Nanjing University, Nanjing 210093, PR China b The Institute of Mathematical Sciences, CUHK, Shatin, N.T., Hong Kong c Department of Mathematics and IMS, CUHK, Shatin, N.T., Hong Kong |
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Abstract: | In this paper, we establish the existence and stability of a 3-D transonic shock solution to the full steady compressible Euler system in a class of de Laval nozzles with a conic divergent part when a given variable axi-symmetric exit pressure lies in a suitable scope. Thus, for this class of nozzles, we have solved such a transonic shock problem in the axi-symmetric case described by Courant and Friedrichs (1948) in Section 147 of 8]: Given the appropriately large exit pressure pe(x), if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed so that the position and the strength of the shock front are automatically adjusted such that the end pressure at the exit becomes pe(x). |
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Keywords: | 35L70 35L65 35L67 76N15 |
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