Communications in Mathematical Sciences

Volume 19 (2021)

Number 4

Radon measure solutions for steady hypersonic-limit Euler flows passing two-dimensional finite non-symmetric obstacles and interactions of free concentration layers

Pages: 875 – 901



Aifang Qu (Department of Mathematics, Shanghai Normal University, Shanghai, China)

Li Wang (Department of Arts and Sciences, Shanghai Dianji University, Shanghai, China)

Hairong Yuan (Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, China)


By proposing a notion of Radon measure solutions of the compressible Euler equations, we consider in the paper uniform stationary hypersonic-limit flows passing a two-dimensional finite non-symmetric obstacle with static gas downstream behind the obstacle, and construct solutions with mass concentrated on the boundary of the obstacle and then on free layers beyond it. The Newton–Busemann pressure law on lifts/drags of the obstacle in hypersonic flow is rigorously derived. The pressure of the static gas influences the structure of the solution. Both terminations and interactions of the free concentration layers may be possible. We give some criterions about it and also present some numerical examples to demonstrate these possibilities.


radon measure solution, compressible Euler equations, pressureless gas, hypersonic flow, Newton–Busemann pressure law, initial-boundary value problem

2010 Mathematics Subject Classification

35L65, 35L67

Received 11 July 2020

Accepted 4 November 2020

Published 18 June 2021