On a fluid-structure interaction problem for plaque growth

TL;DR

This paper investigates a complex fluid-structure interaction model involving blood vessel plaque growth, combining Navier-Stokes fluid dynamics, viscoelastic structural behavior, and biochemical growth processes, establishing well-posedness of the nonlinear system.

Contribution

It introduces a mathematical framework for a fluid-structure interaction with growth, proving well-posedness using maximal regularity and contraction mapping.

Findings

Proved well-posedness of the nonlinear fluid-structure-growth model.

Applied maximal regularity theory to a linearized version of the problem.

Established existence and uniqueness of solutions for the complex model.

Abstract

We study a free-boundary fluid-structure interaction problem with growth, which arises from the plaque formation in blood vessels. The fluid is described by the incompressible Navier-Stokes equation, while the structure is considered as a viscoelastic incompressible neo-Hookean material. Moreover, the growth due to the biochemical process is taken into account. Applying the maximal regularity theory to a linearization of the equations, along with a deformation mapping, we prove the well-posedness of the full nonlinear problem via the contraction mapping principle.