A transformation theory of the partial differential equations of gas dynamics

Charles Loewner
Apr 1950

A transformation theory of systems of partial differential equations is developed which allows the construction of classes of pressure-density relations depending on arbitrarily many parameters for which the equations governing the flow can be transformed into an essentially simpler form, namely, into the Cauchy-Riemann equations in the subsonic region, into the system corresponding to the wave equation in the supersonic case, and finally into that form corresponding to the Tricomi equation in the transonic region.

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