The existence and monotonicity of a three-dimensional transonic shock in a finite nozzle with axisymmetric exit pressure

Jun Li, Zhouping Xin and Huicheng Yin

Vol. 247 (2010), No. 1, 109–162

DOI: 10.2140/pjm.2010.247.109

Abstract

We establish the existence of a multidimensional transonic shock solution in a class of slowly varying nozzles for the three dimensional steady full Euler system with axially symmetric exit pressure in the diverging part lying in an appropriate scope. We also show that the shock position depends monotonically on the exit pressure.

Keywords

steady Euler system, multidimensional transonic shock, axisymmetric, first order elliptic system

Mathematical Subject Classification 2000

Primary: 35L65, 35L67, 35L70

Secondary: 76N15

Milestones

Received: 8 June 2009

Accepted: 16 January 2010

Published: 1 July 2010