学术报告 报告题目1：Non-existence of 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：Boundary Layer Problem and Zero Viscosity-Diffusion Vanishing Limit of the Incompressible Magnetohydrodynamic System with No slip Dirichlet Boundary 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：
It is an open problem to show the well-posedness of classical solution to compressible Navier-Stokes equations with the density possibly containing vacuum, although the same problem has been proved by Nash and Serrin in energy space in 1960s when the vaccum is excluded. In this talk, we shall prove that there does not exit any classical solution with density being compact supported to the Cauchy problem for one-dimensional compressible Navier-Stokes equaions in energy space so long as the initial data satisfy some properties.
报告2摘要：
In this talk, we will talk about the boundary layer problem and zero viscositydiffusion vanishing limit of the initial boundary value problem for the incompressible viscous and diffusive magnetohydrodynamic(MHD) system with Dirichlet boundary (no-slip characteristic)conditions and will prove that the incompressible inviscid MHD system and the related Prandtl boundary layer are stable with respect to the viscosity and magnetic diffusion coefficients. The main difficulty here comes from the Dirichlet boundary condition for the velocity and magnetic field. Firstly, we consider the classical Prandtlboundary layer problem for MHD system with a class of special initial data.We establish the result on the stability of the Prandtl boundary layer of MHD system and prove rigorously the solution of incompressible viscous-diffusion MHD system converges to the sum of the solution to the ideal inviscid MHD system and the approximating solution to Prandtl boundary layer equation by using the elaborate energy methods and the special structure of the solution to inviscid MHD system, which yields that there exists the cancelation between the boundary layer of the velocity and the one of the magnetic field. Secondly, for general initial data, we consider the boundary layer problem of the incompressible viscous and diffusive MHD system with the different horizontal and vertical viscosities and magnetic diffusions, when they go to zero with the different speeds. We prove rigorously the convergence to the ideal inviscid MHD system and the anisotropic inviscid MHD system from the incompressible viscous and diffusion MHD system by constructing the exact boundary layers and using the elaborate energy methods. We also mention that these results obtained here should be the first rigorous ones on the stability of Prandtl boundary layer for the incompressibleviscous and diffusion MHD system with no-slip characteristic boundary condition.