中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：闫伟 教授（吉林大学）
题 目：Steady Subsonic flows in High Dimensional Nozzle
时 间：2023.11.13（星期一）上午09:00-10:00
地 点：腾讯会议：914-246-271
摘 要：In this talk, we present our result on subsonic irrotational flows in a multi-dimensional (n>1) infinitely long nozzle with variable cross sections. The flow is described by the inviscid potential equation, which is a second order quasilinear elliptic equation when the flow is subsonic. We prove the existence and the uniqueness of the global uniformly subsonic flow in a general infinitely long nozzle of arbitrary dimension. Furthermore, we show that there exists a critical value of the incoming mass flux such that a global uniformly subsonic flow exists uniquely, provided that the incoming mass flux is less than the critical value. This gives a positive answer to the problem of L. Bers.
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报告人：闫伟 教授（吉林大学）
题 目：Blowup of smooth solutions for compressible Navier-Stokes equations
时 间：2023.11.13（星期一）上午10:00-11:00
地 点：腾讯会议：914-246-271
摘 要：In this talk，we discuss the finite time blow up phenomena of smooth solutions to the compressible Navier-Stokes system when the initial data contain vacuums. It is proved that any classical solutions of viscous compressible fluids without heat conduction will blow up in finite time, as long as the initial data has an isolated mass group. The results hold regardless of either the size of the initial data or the far fields being vacuum or not. This improves the blowup results of Xin（CPAM，1998） by removing the crucial assumptions that the initial density has compact support and the smooth solution has finite total energy. Furthermore, the analysis here also yields that any classical solutions of viscous compressible fluids without heat conduction in bounded domains or periodic domains will blow up in finite time, if the initial data have an isolated mass group satisfying some suitable conditions.
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