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
综合报告
报告人： 石佳 博士（MIT）
题 目：Integrodifferential equations for fluids in two dimensions
时 间：2023.06.02（星期五），09:00-10:00
地 点：Zoom会议：883 9098 6393 密码：0602
摘 要：We will talk about two problems related with Integrodifferential equations. The first one is on the analyticity of the solutions to the Muskat equation. The Muskat equation describes the interface of two liquids in a porous medium.We will show that if a solution to the Muskat problem is sufficiently smooth, then it must be analytic except at the points where a turnover of the fluids happens. We will also show analyticity in a region that degenerates at the turnover points provided someadditional conditions are satisfied. The other problem studies the radial symmetry properties of stationary and uniformly rotating solutions of the 2D Euler/g-SQG equations. We will show some rigidity results giving conditions under which the solutions must be radial. We will also show some flexibilityresults: the existence of non-radial solutions. The results on this second problem are joint work with Javier Gomez-Serrano, Jaemin Park and Yao Yao.
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