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The Peskin problem with viscosity contrast

Eduardo García-Juárez, Yoichiro Mori and Robert M. Strain

Vol. 16 (2023), No. 3, 785–838

The Peskin problem models the dynamics of a closed elastic filament immersed in an incompressible fluid. We consider the case when the inner and outer viscosities are possibly different. This viscosity contrast adds further nonlocal effects to the system through the implicit nonlocal relation between the net force and the free interface. We prove the first global well-posedness result for the Peskin problem in this setting. The result applies for medium-size initial interfaces in critical spaces and shows instant analytic smoothing. We carefully calculate the medium-size constraint on the initial data. These results are new even without viscosity contrast.

Peskin problem, fluid-structure interface, viscosity contrast, global regularity, critical regularity, immersed boundary problem, Stokes flow, fractional Laplacian, solvability, stability
Mathematical Subject Classification
Primary: 35Q35, 35C15, 35R11, 35R35, 76D07
Secondary: 35C10
Received: 16 December 2020
Revised: 6 July 2021
Accepted: 23 August 2021
Published: 25 May 2023
Eduardo García-Juárez
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes
Yoichiro Mori
Department of Mathematics
University of Pennsylvania
David Rittenhouse Lab
Philadelphia, PA
United States
Robert M. Strain
Department of Mathematics
University of Pennsylvania
David Rittenhouse Lab
Philadelphia, PA
United States

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