Évènements

Simulating and modeling flexible fibers is an crucial issue in many microbiological problems. We focus on a recent result on convergence and well-posedness of the equations governing the dynamics of a discretized version of a continuous, flexible, inextensible filament immersed in a fluid at a low-Reynolds number.
The elastohydrodynamic equation governing the motion of such a filament is a nonlinear 4th-order PDE system. Complexity in analytical and numerical study of the system has led to the use of simplified models, e.g. the ”N-link” [F. Alouges, A. DeSimone, L. Giraldi, M. Zoppello, Self-propulsion of slender microswimmers by curvature control : N-link swimmers, Int. J. Non-Linear Mech.,2013.], a mechanical discretization into N rigid segments with elastic joints.
While numerical evidence shows convergence of this model to the continuous case [C. Moreau, L. Giraldi, H. Gadˆelha, The asymptotic coarse-graining formulation of slender-rods, bio-filaments and flagella, J. R. Soc. Interface, 2018], rigorous convergence is nontrivial: the equations of the N-link are not a classical approximation of the underlying PDE.
We prove existence and uniqueness of solutions for the N-link system and demonstrate their convergence to solutions of the classical PDE, leading also to an alternative proof of existence for the continuous PDE, complementing [Y. Mori, L. Ohm, Well-posedness and applications of classical elastohydrodynamics for a swimming filament, Nonlinearity, 2023].
This work was done in collaboration with F. Alouges, A. Lefebvre-Lepot and C. Moreau.