Global Solutions for Supersonic Flow Past a Delta Wing

In this paper we study the mathematical aspects of supersonic flow past a delta wing. The flow is described by the potential flow equation, and the delta wing is assumed to be a triangular plate or a triangular wing with specific thickness. In the self-similar coordinates, the problem can be reduced to a boundary value problem of a nonlinear degenerate elliptic equation with a free boundary. By constructing a nonlinear iteration scheme and applying the Schauder fixed point theorem, we prove the existence of a solution to this problem, provided that the incident angle of the oncoming flow is less than a critical value determined by the data.

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