中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人： 石佳 博士（MIT）
题 目：On the analyticity of the Muskat equation
时 间：2023.06.07（星期三），09:00-10:00
地 点：腾讯会议：895 671 371
摘 要：We will continue to talk about the analyticity of the solutions to the Muskat equation. First, we will derive the interface equation from Darcy's law. Next, we will show why the linear model fits and the corresponding parabolic behavior. Then we will provide more details on how to show the analyticity/degenerated analyticity of the solution. The main ingredients include the localization techniques, the energy estimates and estimates for the commutator between the integral operator and Cauchy-Riemann operator. We will also show that the method can be applied to more general cases.
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报告人： 石佳 博士（MIT）
题 目：The radial symmetry properties of stationary and uniformly rotating solutions of the 2D Euler/g-SQG equations
时 间：2023.06.08（星期四），09:00-10:00
地 点：腾讯会议：458 952 291
摘 要：We will continue to discuss the radial symmetry of the stationary and uniformly rotating solutions of the 2D Euler/g-SQG equations. We will give a complete proof for the rigidity results of simply connected patch solutions and a sketch proof for the non-simply connected case. Then we will move on to the flexibility results for 2D-Euler. We will introduce how we apply the bifurcation theory and the Nash-Moser iteration to show the existence of non-radial stationary patches with finite/infinite energy. The results are joint work with Javier Gomez-Serrano, Jaemin Park and Yao Yao.
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