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The Peskin problem
with viscosity contrast
Eduardo García-Juárez, Yoichiro Mori and Robert M. Strain |
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Vol. 16 (2023), No. 3, 785–838
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Abstract |
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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. |
Keywords
Peskin problem, fluid-structure interface, viscosity
contrast, global regularity, critical regularity, immersed
boundary problem, Stokes flow, fractional Laplacian,
solvability, stability
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Mathematical Subject Classification
Primary: 35Q35, 35C15, 35R11, 35R35, 76D07
Secondary: 35C10
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Milestones
Received: 16 December 2020
Revised: 6 July 2021
Accepted: 23 August 2021
Published: 25 May 2023
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Authors |
| Eduardo García-Juárez | |
| Departament de Matemàtiques i
Informàtica Universitat de Barcelona Gran Via de les Corts Catalanes Barcelona Spain |
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| Yoichiro Mori | |
| Department of Mathematics University of Pennsylvania David Rittenhouse Lab Philadelphia, PA United States |
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| Robert M. Strain | |
| Department of Mathematics University of Pennsylvania David Rittenhouse Lab Philadelphia, PA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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