English

Global weak solutions to a 3D/3D fluid-structure interaction problem including possible contacts

Analysis of PDEs 2023-12-20 v3

Abstract

In this paper, we study an interaction problem between a 3D3D compressible viscous fluid and a 3D3D nonlinear viscoelastic solid fully immersed in the fluid, coupled together on the interface surface. The solid is allowed to have self-contact or contact with the rigid boundary of the fluid container. For this problem, a global weak solution with defect measure is constructed by using a multi-layered approximation scheme which decouples the body and the fluid by penalizing the fluid velocity and allowing the fluid to pass through the body, while the body is supplemented with a contact-penalization term. The resulting defect measure is a consequence of pressure concentrations that can appear where the fluid meets the (generally irregular) points of self-contact of the solid. Moreover, we study some geometrical properties of the fluid-structure interface and the contact surface. In particular, we prove a lower bound on area of the interface.

Keywords

Cite

@article{arxiv.2304.11809,
  title  = {Global weak solutions to a 3D/3D fluid-structure interaction problem including possible contacts},
  author = {Malte Kampschulte and Boris Muha and Srđan Trifunović},
  journal= {arXiv preprint arXiv:2304.11809},
  year   = {2023}
}
R2 v1 2026-06-28T10:15:17.259Z