## Abstract

Consider an inextensible closed filament immersed in a 2D Stokes fluid. Given a force density F defined on this filament, we consider the problem of determining the tension σ on this filament that ensures the filament is inextensible. This is a subproblem of dynamic inextensible vesicle and membrane problems, which appear in engineering and biological applications. We study the well-posedness and regularity properties of this problem in Hölder spaces. We find that the tension determination problem admits a unique solution if and only if the closed filament is not a circle. Furthermore, we show that the tension σ gains one derivative with respect to the imposed line force density F and show that the tangential and normal components of F affect the regularity of σ in different ways. We also study the near singularity of the tension determination problem as the interface approaches a circle and verify our analytical results against numerical experiment.

Original language | English |
---|---|

Article number | 46 |

Journal | Research in Mathematical Sciences |

Volume | 10 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2023 |

## Keywords

- Boundary integral equation
- Hölder regularity
- Inextensible interface
- Interfacial tension
- Stokes flow