A degenerate elliptic problem from subsonic-sonic flows in convergent nozzles

Abstract

<p style="text-indent:20px;">This paper concerns continuous subsonic-sonic potential flows in a two dimensional convergent nozzle, which is governed by a free boundary problem of a quasilinear degenerate elliptic equation. It is shown that for a given nozzle which is a perturbation of an straight one, and a given mass flux, there exists uniquely a continuous subsonic-sonic flow whose velocity vector is along the normal direction at the inlet and the sonic curve. Furthermore, the sonic curve of this flow is a free boundary, where the flow is singular in the sense that the speed is only <inline-formula><tex-math id="M1">\begin{document}$ C^{1/2} $\end{document}</tex-math></inline-formula> Hölder continuous and the acceleration blows up at the sonic state.</p>