中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
报告人：黎 勇 教授 (北京工业大学)
题 目：Quasi-neutral limit of the two-fluid Euler-Poisson system in a domain with boundary
时 间：2019.05.23（星期四）, 09:30-10:30
地 点：数学院南楼N205室
摘 要：In this talk, the quasineutral limit of the two-fluid Euler-Poisson system (one for ions and another for electrons) in a bounded domain of R3 is rigorously proved by investigating the existence and the stability of boundary layers. The non-penetration boundary condition for velocities and Dirichlet boundary condition for electric potential are considered. This is a joint work with Prof. Qiangchang Ju.
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报告人：Dr. Chenyun Luo (Vanderbilt University, USA)
题 目：Local well-posedness for the motion of a compressible, self-gravitating liquid droplet with free surface boundary
时 间：2019.05.23（星期四）, 15:00-16:00
地 点：数学院南楼N602室
摘 要：We establish the local well-posedness for the free boundary problem for the compressible Euler equations describing the motion of liquid under the influence of Newtonian self-gravity. We do this by solving a tangentially-smoothed version of Euler's equations in Lagrangian coordinates which satisfies uniform energy estimates as the smoothing parameter goes to zero. The main technical tools are delicate energy estimates and optimal elliptic estimates in terms of boundary regularity, for the Dirichlet problem and Green's function.
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报告人：Dr. Junyan Zhang (Johns-Hopkins University, USA)
题 目：On the incompressible free-boundary MHD with or without surface tension
时 间：2019.05.23（星期四）, 16:00-17:00
地 点：数学院南楼N602室
摘 要：We present a priori estimates for the incompressible MHD equations in a bounded domain with free moving boundary. In the case of no surface tension, higher regularity of the flow map is required due to a loss of 1/2-order derivative in the low regularity estimates. Due to the lack of Cauchy invariance for MHD, the smallness assumption on the fluid domain is required to control the vorticity of the flow map to compensate this loss. While in the case of nonzero surface tension, the flow map can be controlled by the boundary elliptic estimates owing to the surface tension. Moreover, we show that the magnetic field has certain regularizing effect, allowing us to control the vorticity of the fluid and that of the magnetic field simultaneously. This is the joint work with Dr. Chenyun Luo.
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