Well-posedness and global behavior of the Peskin problem

Speaker

Time

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 $VM{O}^1$ satisfying the so-called well-stretched assumption. Then, we will show that when the initial string configuration is sufficiently close to an equilibrium in $BM{O}^1$, global-in-time solution uniquely exists and it will converge to an equilibrium as $t\to \mathrm{\infty }$. This is based on a joint work with Prof. Quoc-Hung Nguyen.