Continuous subsonic-sonic flows in convergent nozzles with straight solid walls
Yuanyuan Nie, Chunpeng Wang · Nonlinearity · 2015
Abstract This paper concerns continuous subsonic-sonic potential flows in a two-dimensional convergent nozzle with straight solid walls. It is shown that for the given inlet, which is a perturbation of an arc centered at the vertex of the nozzle, and the given incoming flow angle which is a perturbation of the angle of the inner normal of the inlet, and the 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 given incoming flow angle and the given incoming mass flux. Furthermore, the sonic curve of this flow is a free boundary, where the flow is singular in the sense that the speed is only Hölder continuous and the acceleration blows up at the sonic state. The perturbation problem is solved in the potential plane, where the flow is governed by a degenerate elliptic problem with two free boundaries, on one of which the equation is degenerate and on the other of which the boundary condition is nonlocal.