Communications in Mathematical Sciences
Volume 20 (2022)
On two-dimensional steady hypersonic-limit Euler flows passing ramps and radon measure solutions of compressible Euler equations
Pages: 1331 – 1361
We proposed rigorous definitions of Radon measure solutions for boundary value problems of steady compressible Euler equations which model hypersonic-limit inviscid flows passing two-dimensional ramps, and their interactions with still gas and pressureless jets. We proved the Newton–Busemann pressure law of drags on a body in hypersonic flow, and constructed various physically interesting measure solutions with density containing Dirac measures supported on curves, also exhibited examples of blow up of certain measure solutions. This established a mathematical foundation for applications in engineering and further studies of measure solutions of compressible Euler equations.
compressible Euler equations, hypersonic, Newton–Busemann pressure law, shock layer, free layer, Dirac measure, measure solution, vacuum, singular Riemann problem
2010 Mathematics Subject Classification
35L65, 35L67, 35Q31, 35R06, 35R35, 76K05
The research of Aifang Qu is supported by National Natural Science Foundation of China (NNSFC) under Grants No.11571357, No.11871218, and No.12071298.
Hairong Yuan is supported by NNSFC under Grants No.11871218, No.12071298, and by Science and Technology Commission of Shanghai Municipality (STCSM) under Grant No. 18dz2271000.
Received 20 August 2021
Accepted 30 November 2021
Published 26 May 2022