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

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[arXiv preprint: .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.

On a fluid–structure interaction problem for plaque growth

“…We remark here that if the domain is not smooth enough, for example, with boundary contact, it is still an open problem. The authors considered a similar model with ninety degree contact angles in [3] recently.…”

“…Theorem 3.1. Let q > n + 2, T > 0, Ω a bounded domain as before with Γ s ∈ C 3 , Γ a closed hypersurface of class C 3 . Assume that (k, g, h 1 , h 2 ) are known functions contained in Z v T with initial value zero and v0 ∈ D 1 q with compatibility conditions…”

“…Proposition A.1. Let q > n + 2, Ω ⊂ R n be a bounded domain with ∂Ω ∈ C 3 , Σ ⊂ Ω a closed hypersurface of class C 3 . Assume that (f u , g d , g b , g u , g) ∈ Z T where…”