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What is a formal proof for Kutta-Joukowski Theorem in compressible flow?

Physics Asked by JZYL on December 14, 2020

Texts, such as Drela, Flight Vehicle Aerodynamics, indicate that the Kutta-Joukowski Theorem holds in compressible flow. Indeed, the KJT seems hold in linearized supersonic flow around a 2D flat plate. However, the proof that I find on Wikipedia relies on assuming that the flow is incompressible and that the total pressure remains constant.

Is there a formal proof that shows the KJT works in compressible flow, or supersonic flow where shock is present (across which total pressure changes)?

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