On Multi-Dimensional Sonic-Subsonic Flow

Feimin Huang; Tianyi Wang; Yong Wang

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arXiv · 1103.0078

On Multi-Dimensional Sonic-Subsonic Flow

Feimin Huang·Tianyi Wang·Yong Wang

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Abstract

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

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Feimin Huang, Tianyi Wang, Yong Wang. 2011-03-01. On Multi-Dimensional Sonic-Subsonic Flow. https://arxiv.org/abs/1103.0078

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