On multi-dimensional sonic-subsonic flow

In this paper, a compensated compactness framework is established for sonic-subsonic approximate solutions to the n-dimensional (n ≥ 2) Euler equations for steady irrotational flow that may contain stagnation points. This compactness framework holds provided that the approximate solutions are uniformly bounded and satisfy H−1loc (Ω) com pactness conditions. As illustration, we show the existence of sonic-subsonic weak solution to n-dimensional (n ≥ 2) Euler equations for steady irrotational flow past obstacles or through an infinitely long nozzle. This is the first result concerning the sonic-subsonic limit for n-dimension (n ≥ 3).