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：Prof. Nguyen Quoc-Hung (Institute of Mathematical Sciences, ShanghaiTech Univerisity)
题 目：Well-posedness of the Muskat problem
时 间：2021.05.21（星期五）, 16:00-17:00
地 点：数学院南楼N219室
Zoom 会议：412 019 4771，密码：mcm1234
https://zoom.com.cn/j/4120194771?pwd=NXRnZGhyTWRzVDJwNWwyR0IwQWlNdz09
摘 要：The Muskat problem is a classical mathematical model which describes the motion of two immiscible and incompressible Newtonian fluids in an homogeneous porous medium. The mathematical model posed in the entire plane can be formulated as an evolution equation for the function that parametrizes the free boundary between the fluids. In this talk, I will present local/global well-posedness results for the 2d/3d Muskat problem in critical spaces. Moreover, I will also discuss a toy model for the 2d Muskat which is globally well-posed for large data in a supercritical space. This is based on works in collaboration with Thomas Alazard, Omar Lazar, Ke Chen, Yiran Xu and Stephen Cameron. After this talk, I will present an overview of my works and my future works.
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