Abstract
The problem of finding steady flow past an airfoil is an old problem going back to the time of Lord Rayleigh. The understanding that there was a difficulty connected to the transition from subsonic flow to supersonic flow must surely, however, be attributed to Chaplygin [1], whose famous thesis describing solutions of the equations with such transitions was written in 1904. The first mathematical study of such transitions which force a change of type for the differential equations from elliptic to hyperbolic began with the work of Tricomi [2] in 1923. In 1930 at the International Mechanics Congress, Busemann [3] with wind tunnel data, and G.I. Taylor [4] with some computations, presented opposing views of the airfoil problem, the former suggesting that perhaps no steady flow existed and the latter than a series expansion in Mach number gave no evidence of a breakdown when the type changed.
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References
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Morawetz, C.S. (1987). Transonic Flow and Compensated Compactness. In: Chorin, A.J., Majda, A.J. (eds) Wave Motion: Theory, Modelling, and Computation. Mathematical Sciences Research Institute Publications, vol 7. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9583-6_9
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