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Vaccum dynamics of the viscous compressible Navier-Stokes equations - 黄祥娣 副研究员(中科院)

作者:   来源:  时间:2019-08-25

Title: Vaccum dynamics of the viscous compressible Navier-Stokes equations .

讲课人:黄祥娣 副研究员(中科院)

Abstract:

   In this mini course, we will review the classical well-posed theory of the weak and strong solutions to the multi-dimensional compressible fluids, including the insentropic Navier-Stokes equations and viscous heat-conduting Navier-Stokes-Fourier system. 
  In the absence of vacuum, local and global existence theory were well-established since Kanel's pioneer work and later by a series of subsequent important works. Things become more complicated when vacuum region appears.
  Generally speaking, the smooth solutions will lose their regularities in finite time when the density is allowed to vanish in some region. It is natural to ask what kind of physical mechanism should be responisible for the blowup of the classical solutions in finite time.
  We will concentrate on the behavior of the weak and classical solutions in the presence of vacuum. Based on some crucial 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.

时间:8月15号开始,每周三周四9-11点

地点:首师大新教二楼527教室

邀请人:牛冬娟