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

DOI: 10.2140/pjm.2011.254.129

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