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Smooth Transonic Flows in De Laval Nozzles

發布者:文明辦發布時間:2019-04-18瀏覽次數:1127


主講人:王春朋 吉林大學數學學院教授 博士生導師


時間:2019年4月19日14:00


地點:3號樓3樓332報告廳


舉辦單位:數理學院


主講人介紹:吉林大學數學學院教授、博士生導師,國家自然科學基金優秀青年科學基金獲得者、教育部新世紀優秀人才、吉林省長白山學者特聘教授、全國百篇優秀博士學位論文獎獲得者。從事偏微分方程領域的研究,近年來圍繞可壓流體的跨音速流動理論,研究包含音速狀態的流體流動模型以及非線性奇異偏微分方程的定性理論。多次應邀到香港中文大學、香港城市大學和意大利ICTP研究中心做學術訪問。合作出版中文專著和英文專著各一部,發表學術論文近60余篇。


內容介紹: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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