On a fluid-structure interaction problem for plaque growth: cylindrical domain

TL;DR

This paper studies a complex fluid-structure interaction model for plaque growth in cylindrical domains, establishing existence and uniqueness of solutions with added viscoelastic effects, advancing mathematical understanding of such biological systems.

Contribution

It introduces a new analysis of a plaque growth model in cylindrical domains with contact angles, proving local well-posedness of the nonlinear system.

Findings

Existence and uniqueness of strong solutions for the linearized system.

Well-posedness of the nonlinear system in cylindrical domains.

Application of reflection and localization techniques to handle domain geometry.

Abstract

This paper concerns a free-boundary fluid-structure interaction problem for plaque growth proposed by Yang et al. [J. Math. Biol., 72(4):973--996, 2016] with additional viscoelastic effects, which was also investigated by the authors [arXiv preprint: 2110.00042, 2021]. Compared to it, the problem is posed in a cylindrical domain with ninety-degree contact angles, which brings additional difficulties when we deal with the linearization of the system By a reflection argument, we obtain the existence and uniqueness of strong solutions to the model problems for the linear systems, which are then shown to be well-posed in a cylindrical (annular) domain via a localization procedure. Finally, we prove that the full nonlinear system admits a unique strong solution locally with the aid of the contraction mapping principle.