Critical well-posedness for the 2D Peskin problem with general tension

Eduardo García-Juárez; Susanna V. Haziot

doi:10.1016/j.aim.2024.110047

Critical well-posedness for the 2D Peskin problem with general tension

Eduardo García-Juárez, Susanna V. Haziot

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we study the two dimensional Peskin problem with general elasticity law. Specifically, we prove global regularity for small perturbations, in suitable critical spaces, of the circle solution, possibly containing corners. For such initial data we prove asymptotic stability in the sense that as t→∞, the solution converges to a translated and rotated disk.

Original language	English (US)
Article number	110047
Journal	Advances in Mathematics
Volume	460
DOIs	https://doi.org/10.1016/j.aim.2024.110047
State	Published - Jan 2025

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Corner
Critical regularity
Immersed boundary
Peskin

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10.1016/j.aim.2024.110047

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title = "Critical well-posedness for the 2D Peskin problem with general tension",

abstract = "In this paper, we study the two dimensional Peskin problem with general elasticity law. Specifically, we prove global regularity for small perturbations, in suitable critical spaces, of the circle solution, possibly containing corners. For such initial data we prove asymptotic stability in the sense that as t→∞, the solution converges to a translated and rotated disk.",

keywords = "Corner, Critical regularity, Immersed boundary, Peskin",

author = "Eduardo Garc{\'i}a-Ju{\'a}rez and Haziot, \{Susanna V.\}",

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year = "2025",

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doi = "10.1016/j.aim.2024.110047",

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AU - García-Juárez, Eduardo

AU - Haziot, Susanna V.

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N2 - In this paper, we study the two dimensional Peskin problem with general elasticity law. Specifically, we prove global regularity for small perturbations, in suitable critical spaces, of the circle solution, possibly containing corners. For such initial data we prove asymptotic stability in the sense that as t→∞, the solution converges to a translated and rotated disk.

AB - In this paper, we study the two dimensional Peskin problem with general elasticity law. Specifically, we prove global regularity for small perturbations, in suitable critical spaces, of the circle solution, possibly containing corners. For such initial data we prove asymptotic stability in the sense that as t→∞, the solution converges to a translated and rotated disk.

KW - Corner

KW - Critical regularity

KW - Immersed boundary

KW - Peskin

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DO - 10.1016/j.aim.2024.110047

M3 - Article

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VL - 460

JO - Advances in Mathematics

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M1 - 110047

ER -

Critical well-posedness for the 2D Peskin problem with general tension

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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