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上海市数学会青年学者论坛
——偏微分方程论坛

Well-posedness and global behavior of the Peskin problem

Speaker

陈可 , 复旦大学

Time

18 Dec, 17:00 - 17:40

Abstract

The Peskin problem models the dynamics of a closed elastic filament immersed in an incompressible fluid. In this talk we will present local and global well-posedness results for the 2D Peskin problem in critical spaces. Specifically, we will prove the local well-posedness for any initial data in $VMO^1$ satisfying the so-called well-stretched assumption. Then, we will show that when the initial string configuration is sufficiently close to an equilibrium in $BMO^1$, global-in-time solution uniquely exists and it will converge to an equilibrium as $t\rightarrow \infty$. This is based on a joint work with Prof. Quoc-Hung Nguyen.