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Hyperbolic & Dispersive PDE Seminar

Well-Posedness of the 3D Peskin Problem

Robert Strain (University of Pennsylvania)

Location:  Hill 705
Date & time: Thursday, 23 February 2023 at 3:30PM - 4:30PM

This work introduces the 3D Peskin problem: a two-dimensional elastic membrane immersed in a three-dimensional steady Stokes flow. This work obtains the equations that model this free boundary problem and shows that these equations admit a boundary integral reduction, providing an evolution equation for the elastic interface. We consider general nonlinear elastic laws, i.e., the fully nonlinear 3D Peskin problem, and we prove that the problem is well-posed in low-regularity Hölder spaces. Moreover, we prove that the elastic membrane becomes smooth instantly in time. This is a joint work with Eduardo García-Juárez, Po-Chun Kuo, and Yoichiro Mori.

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