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Radon measure solutions for steady compressible hypersonic-limit Euler flows passing cylindrically symmetric conical bodies

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    * Corresponding author

The research of Aifang Qu is supported by the 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 the Science and Technology Commission of Shanghai Municipality (STCSM) under Grant No. 18dz2271000

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  • We study steady uniform hypersonic-limit Euler flows passing a finite cylindrically symmetric conical body in the Euclidean space $ \mathbb{R}^3 $, and its interaction with downstream static gas lying behind the tail of the body. Motivated by Newton's theory of infinite-thin shock layers, we propose and construct Radon measure solutions with density containing Dirac measures supported on surfaces and prove the Newton-Busemann pressure law of hypersonic aerodynamics. It happens that if the pressure of the downstream static gas is quite large, the Radon measure solution terminates at a finite distance from the tail of the body. The main difficulty of the analysis is a correct definition of Radon measure solutions. The results are helpful to understand mathematically some physical phenomena and formulas about hypersonic inviscid flows.

    Mathematics Subject Classification: Primary: 35L65, 35L67, 35Q31, 35R06, 35R35; Secondary: 76K05.

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  • Figure 1.  The upstream hypersonic-limit flow is separated from the downstream static gas by an axially-symmetric free concentration interface

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