Transonic Flow and Compensated Compactness
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 , 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  in 1923. In 1930 at the International Mechanics Congress, Busemann  with wind tunnel data, and G.I. Taylor  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.
KeywordsMach Number Steady Flow Supersonic Flow Entropy Condition Compressible Fluid
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