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Title: Critical local well‐posedness for the fully nonlinear Peskin problem
Abstract We study the problem where a one‐dimensional elastic string is immersed in a two‐dimensional steady Stokes fluid. This is known as the Stokes immersed boundary problem and also as the Peskin problem. We consider the case with equal viscosities and with a fully non‐linear tension law; this model has been called the fully nonlinear Peskin problem. In this case we prove local in time wellposedness for arbitrary initial data in the scaling critical Besov space . We additionally prove the optimal higher order smoothing effects for the solution. To prove this result we derive a new formulation of the boundary integral equation that describes the parametrization of the string, and we crucially utilize a new cancelation structure.  more » « less
Award ID(s):
2055271 2408264
PAR ID:
10518684
Author(s) / Creator(s):
;
Publisher / Repository:
ArXiv
Date Published:
Journal Name:
Communications on Pure and Applied Mathematics
Volume:
77
Issue:
2
ISSN:
0010-3640
Page Range / eLocation ID:
901 to 989
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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