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报告题目： Localclassical solutions to the Compressible Isentropic Navier-StokesEquations with density-dependent viscosities and vacuum
报告人：李亚纯教授（上海交通大学）
报告时间：2016年5月13日（周五）上午10：30-11：30
报告地点：4号楼4318室

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                                                                    数学学院

                                                                  2016年05月11日

报告摘要:
   We investigate the Navier-Stokes equations for multi-dimensionalcompressible  isentropic flow with vacuum appearing in some openset or at the far field. We first establish the local-in-timewell-posedness of the unique regular solution to the compressibleNavier-Stokes equations with density-dependent viscosities in a powerlaw and with vacuum, whose life span is uniformly positive withrespect to the viscosity coefficients. Then we prove that our regularsolution will blow up in finite time under two kinds of blow-upmechanisms. Finally we consider the vanishing viscosity limit byestablishing uniform energy-type estimates with respect to theviscosity coefficients for the regular solutions, which leads to theconvergence of the regular solution of the Navier-Stokes equations tothat  of the  Euler equations with arbitrarily large datawith vacuum.