学术报告报告题目1：Non-existenceof finite energy solution to Compressible Navier-Stokes equations
报告人：李海梁 教授（首都师范大学）
报告时间：2016年11月19（星期六）上午10:00-11:00
报告题目2：BoundaryLayer Problem and Zero Viscosity-Diffusion Vanishing Limit of theIncompressible Magnetohydrodynamic System with No slip DirichletBoundary Conditions
报告人：王术 教授（北京工业大学）
报告时间：2016年11月19（星期六）上午11:00-12:00
报告地点：4号楼4318室
欢迎广大师生前往！
数学学院
2016年11月16日
报告1摘要：
Itis an open problem to show the well-posedness of classical solutionto compressible Navier-Stokes equations with the density possiblycontaining vacuum, although the same problem has been proved byNash and Serrin in energy space in 1960s when the vaccum is excluded.In this talk, we shall prove that there does not exit any classicalsolution with density being compact supported to the Cauchy problemfor one-dimensional compressible Navier-Stokes equaions in energyspace so long as the initial data satisfy some properties.
报告2摘要：
Inthis talk, we will talk about the boundary layer problem and zeroviscositydiffusion vanishing limit of the initial boundary valueproblem for the incompressible viscous and diffusivemagnetohydrodynamic(MHD) system with Dirichlet boundary (no-slipcharacteristic)conditions and will prove that the incompressibleinviscid MHD system and the related Prandtl boundary layer are stablewith respect to the viscosity and magnetic diffusion coefficients.The main difficulty here comes from the Dirichlet boundary conditionfor the velocity and magnetic field. Firstly, we consider theclassical Prandtlboundary layer problem for MHD system with a classof special initial data.We establish the result on the stability ofthe Prandtl boundary layer of MHD system and prove rigorously thesolution of incompressible viscous-diffusion MHD system converges tothe sum of the solution to the ideal inviscid MHD system and theapproximating solution to Prandtl boundary layer equation by usingthe elaborate energy methods and the special structure of thesolution to inviscid MHD system, which yields that there exists thecancelation between the boundary layer of the velocity and the one ofthe magnetic field. Secondly, for general initial data, we considerthe boundary layer problem of the incompressible viscous anddiffusive MHD system with the different horizontal and verticalviscosities and magnetic diffusions, when they go to zero with thedifferent speeds. We prove rigorously the convergence to the idealinviscid MHD system and the anisotropic inviscid MHD system from theincompressible viscous and diffusion MHD system by constructing theexact boundary layers and using the elaborate energy methods. We alsomention that these results obtained here should be the first rigorousones on the stability of Prandtl boundary layer for theincompressibleviscous and diffusion MHD system with no-slipcharacteristic boundary condition.