On Multi-Dimensional Sonic-Subsonic Flow

In this paper, a compensated compactness framework is established for sonic-subsonic approximate solutions to the $n$-dimensional$(n\ge 2)$ 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 $H_{loc}^{-1}(\mathrm{\Omega })$ compactness conditions. As illustration, we show the existence of sonic-subsonic weak solution to n-dimensional$(n\ge 2)$ 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$(n\ge 3)$.