This paper concerns the well-posedness of a boundary value problem for a quasilinear second order elliptic equation which is degenerate on a free boundary. Such problems arise when studying continuous subsonic-sonic flows in a convergent nozzle with straight solid walls. It is shown that for a given inlet being a perturbation of an arc centered at the vertex of the nozzle and a given incoming mass flux belonging to an open interval depending only on the adiabatic exponent and the length of the arc, there is a unique continuous subsonic-sonic flow from the given inlet with the angle of the velocity orthogonal to the inlet and the given incoming mass flux. Furthermore, the sonic curve of this continuous subsonic-sonic flow is a free boundary, where the flow is singular in the sense that while the speed is C~(1/2) H?lder continuous at the sonic state, the acceleration blows up at the sonic state.
展开▼
