Year: 2021
Type: preprint
Abstract: In this paper we study the Peskin problem in 2D, which describes the dynamics of a 1D closed elastic structure immersed in a steady Stokes flow. We prove the local well-posedness for arbitrary initial configuration in $(C^2)^{\dot B^1_{\infty,\infty}}$ satisfying the well-stretched condition, and the global well-posedness when the initial configuration is sufficiently close to an equilibrium in $\dot B^1_{\infty,\infty}$. Here $(C^2)^{\dot B^1_{\infty,\infty}}$ is the closure of $C^2$ in the Besov space $\dot B^1_{\infty,\infty}$. The global-in-time solution will converge to an equilibrium exponentially as $t\rightarrow+\infty$. This is the first well-posedness result for the Peskin problem with non-Lipschitz initial data.
Source: arXiv (Cornell University)
Authors: Chen, Ke, Nguyen, Quoc-Hung
Institutions: Academy of Mathematics and Systems Science, Fudan University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G6352055093, G7970755986
OpenAlex ID: W4287063886