中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Prof. Hongjie Dong（Brown University）
题 目：Sobolev estimates for fractional PDEs
时 间：2022.02.10（星期四）21:00-22:00
地 点：Zoom 会议号：924 888 5804 密码：AMSS2022
摘 要：I will discuss some recent results on Sobolev estimates for fractional elliptic and parabolic equations with or without weights. We considered equations with time fractional derivatives of the Caputo type, or with nonlocal derivatives in the space variables, or both. This is based on joint work with Doyoon Kim (Korea University) and Yanze Liu (Brown).
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报告人：Prof.Bogdan-Vasile Matioc（Universität Regensburg）
题 目：The two-phase quasi-stationary Stokes flow by capillarity in the plane
时 间：2022.02.24（星期四）21:00-22:00
地 点：Zoom 会议号：924 888 5804 密码：AMSS2022
摘 要：We discuss a two-phase moving boundary problem that describes the two-dimensional quasistationary Stokes flow of two fluids with different densities and viscosities that occupy the entire plane in the regime where surface tension effects are taken into account at the interface that separates the fluids. In this setting the classical methods of potential theory can be used to transform the model into a nonlinear and nonlocal evolution problem for the function that parameterizes the interface between the fluids, the nonlinearities being expressed by singular integral operators. This problem is of parabolic type, well-posed in all Sobolev spaces up to critical regularity, and it features some parabolic smoothing properties. Joint work with Georg Prokert.
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