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- W4308238265 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 well-posedness for arbitrary initial data in the scaling critical Besov space $dot{B}^{3/2}_{2,1}(mathbb{T} ; mathbb{R}^2)$. 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 cancellation structure." @default.
- W4308238265 created "2022-11-09" @default.
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- W4308238265 date "2021-12-01" @default.
- W4308238265 modified "2023-09-29" @default.
- W4308238265 title "Critical local well-posedness for the fully nonlinear Peskin problem" @default.
- W4308238265 doi "https://doi.org/10.48550/arxiv.2112.00692" @default.
- W4308238265 hasPublicationYear "2021" @default.
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