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Structural stability of transonic shock flows with an external force

Part of: Compressible fluids and gas dynamics, general Hyperbolic equations and systems Equations and systems of special type Transonic flows

Published online by Cambridge University Press:  05 April 2024

Shangkun Weng  and
Wengang Yang
Shangkun Weng
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei Province 430072, People's Republic of China (skweng@whu.edu.cn; yangwg@whu.edu.cn)
Wengang Yang
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei Province 430072, People's Republic of China (skweng@whu.edu.cn; yangwg@whu.edu.cn)
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Abstract

This paper is devoted to the structural stability of a transonic shock passing through a flat nozzle for two-dimensional steady compressible flows with an external force. We first establish the existence and uniqueness of one-dimensional transonic shock solutions to the steady Euler system with an external force by prescribing suitable pressure at the exit of the nozzle when the upstream flow is a uniform supersonic flow. It is shown that the external force helps to stabilize the transonic shock in flat nozzles and the shock position is uniquely determined. Then we are concerned with the structural stability of these transonic shock solutions when the exit pressure is suitably perturbed. One of the new ingredients in our analysis is to use the deformation-curl decomposition to the steady Euler system developed by Weng and Xin [Sci. Sinica Math., 49 (2019), pp. 307–320] to deal with the transonic shock problem.

Keywords

transonic shockstabilization effect of external forcestructural stabilitydeformation-curl decomposition

MSC classification

Primary: 76H05: Transonic flows
Secondary: 35M12: Boundary value problems for equations of mixed type 35L65: Conservation laws 76N15: Gas dynamics, general
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 24
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Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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