Smooth Transonic Flows in De Laval Nozzles


主讲人:王春朋 吉林大学数学学院教授 博士生导师





内容先容:This talk concerns smooth transonic flows of Meyer type in de Laval nozzles,  which are governed by an equation of mixed type with degeneracy at the sonic  state. First we study the properties of sonic curves. For a C2 transonic flow of  Meyer type, the set of exceptional points is shown to be a closed line segment  (may be empty or only one point). The we seek smooth transonic flows of Meyer  type which satisfy physical boundary conditions and whose sonic points are  exceptional. For such a flow, its sonic curve must be located at the throat of  the nozzle and the 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 global extension of this local smooth  transonic flow is also studied. The works are jointed with Professor Zhouping  Xin.

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