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Radon measure solutions for steady compressible Euler equations of hypersonic-limit conical flows and Newton’s sine-squared law.(English)Zbl 1457.76131

In the present work, the authors’ investigations are focused on a special type of uniform upcoming supersonic flowing about a straight cone with a general cross-section and with an attacking angle. The mathematical problem is formulated as a problem on the hypersonic limit of three-dimensional steady uniform non-isentropic compressible Euler flows of polytrophic gases flowing about the above-mentioned cone, that is to study Radon measure solutions of a nonlinear hyperbolic system of conservation laws on the unit 2-sphere. The construction of a measure solution with density containing Dirac measures supported on the surface of the cone is reduced to the problem of finding a regular periodic solution of highly nonlinear and singular ordinary differential equations. For a circular cone with zero attack angle, the authors prove the Newton’s sine-squared flow law by obtaining such a measure solution.

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76K05 Hypersonic flows
35Q31 Euler equations

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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