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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 08, 2023
- Source ID
- 10.1002/cpa.22139
Entities
People
- Robert M Strain
- Stephen Cameron
Organizations
- Intelligence Community Postdoctoral Research Fellowship Program
- University of Pennsylvania