Vol. 254, No. 1, 2011

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Monotonicity and uniqueness of a 3D transonic shock solution in a conic nozzle with variable end pressure

Jun Li, Zhouping Xin and Huicheng Yin

Vol. 254 (2011), No. 1, 129–171
Abstract

We focus on the uniqueness problem of a 3D transonic shock solution in a conic nozzle when the variable end pressure in the diverging part of the nozzle lies in an appropriate scope. By establishing the monotonicity of the position of shock surface relative to the end pressure, we remove the nonphysical assumptions on the transonic shock past a fixed point made in previous studies and further obtain uniqueness.

Keywords
steady Euler system, transonic shock, first-order elliptic system, index of Hilbert problem, maximum principle of weak solutions
Mathematical Subject Classification 2010
Primary: 35L70, 35L65, 35L67, 35L70, 76N15
Milestones
Received: 14 September 2010
Accepted: 28 February 2011
Published: 7 February 2012
Authors
Jun Li
Department of Mathematics and The Institute of Mathematical Sciences
Nanjing University
Nanjing 210093
China
Zhouping Xin
Department of Mathematics and The Institute of Mathematical Sciences
Chinese University of Hong Kong
Shatin
Hong Kong
Huicheng Yin
Department of Mathematics and The Institute of Mathematical Sciences
Nanjing University
Nanjing 210093
China