| Abstract: |
| The Peskin problem describes the motion of an elastic membrane immersed in an incompressible, viscous fluid, typically governed by the Stokes equations. The problem admits a contour dynamics formulation that leads to a nonlinear, nonlocal parabolic PDE. We study the well-posedness in critical spaces and the long-time behaviour of two-dimensional membranes in a three-dimensional fluid for initial interfaces with Lipschitz regularity, which is critical with respect to the natural scaling of the equation. |
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