报告人：王春朋 教授  吉林大学

报告时间：2017.4.26 周三 10:40-11:30

报告地点：知新楼B1044

题目：Smooth Transonic Flows of Meyer Type in De Laval Nozzles

摘要：This talk concerns smooth transonic steady potential flows of Meyer type in two-dimensional de Laval nozzles, which are governed by an equation of mixed type with degeneracy at the sonic state. For a $C^2$ transonic flow of Meyer type, it is shown that the set of exceptional points is a closed line segment (may be empty or only one point). Furthermore, a smooth transonic flow of Meyer type with nonexceptional points is unstable with respect to $C^0$-norm of the velocity for a $C^1$ small perturbation in the shape of the wall (even if the wall is still smooth). Then we seek a smooth transonic flow of Meyer type which satisfies physical boundary condition and whose sonic points are exceptional in a de Laval nozzle. For such a flow, its sonic curve must be located at the throat of the nozzle and the governing equation is strongly degenerate in the sense that the sonic curve is a characteristic degenerate boundary in the subsonic-sonic region, while in the sonic-supersonic region all characteristics from sonic points coincide, which are the sonic curve and never approach the supersonic region. It is proved that there exists uniquely such a smooth transonic flow near the throat of the nozzle, whose acceleration is Lipschitz continuous, if the wall of the nozzle is sufficiently flat. The works are jointed with Professor Zhouping Xin.