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Smooth solutions to the multi-dimensional compressible Navier-Stokes equations in the presence of vacuum. Part II. Nash’s conjecture
发布时间:2018-06-01     点击次数:
报告题目: Smooth solutions to the multi-dimensional compressible Navier-Stokes equations in the presence of vacuum. Part II. Nash’s conjecture
报 告 人: 黄祥娣 研究员(中国科学院数学与系统科学研究所)
报告时间: 2018年06月07日 16:30--17:30
报告地点: 理学院东北楼四楼报告厅(404)
报告摘要:

 In this mini lecture, we will investigate the smooth solutions to the multi-dimensional compressible flows in the presence of vacuum, including the insentropic Navier-Stokes equations and viscous heat-conduting Navier-Stokes-Fourier system.

  Generally speaking, the smooth solutions will lose their regularities in finite time when the density is allowed to vanish in some region. Therefore, we will reveal the possible blowup mechanism which should be responsible for the formation of singularity. Based on these new observations, global in time existence of classical solution with large oscillations and vacuum will be established, which is a sharp constrast to the classical theroy with small perturbation around a non-vacuum resting state.  The method and ideas established so far were proved to be efficient tools in the investigation of compressible framework and will continue to have their value in the future research.

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