Local well-posedness of a three-dimensional phase-field model for thrombus and blood flow

TL;DR

This paper establishes local well-posedness for a 3D phase-field model describing blood flow and thrombus interaction, using a diffuse interface approach and Faedo-Galerkin method.

Contribution

It introduces a novel 3D phase-field model for blood-thrombus interaction and proves its local well-posedness with rigorous a priori estimates.

Findings

Proved local existence and uniqueness of solutions.

Derived key a priori estimates for the model.

Validated the mathematical well-posedness of the phase-field approach.

Abstract

In this article we consider a fluid-structure interactions model on a three dimensional bounded domain, that describes the mechanical interaction between blood flow and a thrombus with Hookean elasticity. The interface between the two phases is given by a smooth transition layer, diffuse with a finite thickness. We derive various a priori estimates and prove local well-posedness results using the Faedo-Galerkin method.