2019年偏微分方程春季研讨会日程
时间:2019年3月29-30日

3月29日下午行健楼665
时间 内容
2:50-4:00 王益(中国科学院数学与系统科学研究院)
Stability of basic wave patterns for some kinetic equations
4:10-5:20 谢峰(上海交通大学)
High Reynolds number limit and boundary layer in MHD
3月30日上午行健楼665
8:50-10:00 王文栋(大连理工大学)
Liouville theorems for the steady Navier-Stokes and MHD equations
10:10-11:20 王玉柱(华北水利水电大学)
Global existence and asymptotic behavior of solutions to the generalized double dispersion equation
 
 
摘  要
Stability of basic wave patterns for some kinetic equations
王益(中国科学院数学与系统科学研究院)
We will first talk about the hydrodynamic limit of classical Boltzmann equation to the compressible Euler equations in the setting of 1D generic Riemann solutions, which is the superposition of three basic wave patterns, i. e., the shock and rarefaction waves and contact discontinuity. Then we will show the nonlinear stability of these three basic wave patterns to the bipolar Vlasov-Poisson-Boltzmann (VPB) systems which describe the motion of the dilute particles under the effect of bipolar electric fields, based on a new micro-macro type decomposition around the local Maxwellian we established for the system, and our most recent result on the time-asymptotic stability of planar rarefaction wave to 3D Boltzmann equation.
High Reynolds number limit and boundary layer in MHD
谢峰(上海交通大学)
In this talk we will recall the classical Prandtl boundary layer multi-scale asymptotical expansions in the analysis of structure of fluids with the high Reynolds number in a domain with boundaries. The Prandtl boundary layer theory includes the well-posedness of solutions to the Prandtl boundary layer equations and the justification of Prandtl boundary layer multi-scale asymptotical expansions. Some known results and analysis tools in the study of characteristic boundary layer will be presented. Then we will give the our results in the study of Prandtl boundary layer for the Magneto Hydrodynamics.
 
 
Liouville theorems for the steady Navier-Stokes and MHD equations
王文栋(大连理工大学)
In this talk, we will recall some recent developments about the steady Navier-Stokes and MHD equations, especially from a Liouville-type perspective. Also, we will talk about our some results on this topic and some remaining questions.
 
 
Global existence and asymptotic behavior of solutions to the generalized double dispersion equation
王玉柱(华北水利水电大学)
In this topic, we state some results on global existence and asymptotic behavior of solutions to the generalized double dispersion equation. The double dispersion model arises in the study of nonlinear wave propagation in waveguide. The results mainly focus on the following two aspects: global solutions and asymptotic behavior of solutions.