A numerical scheme for a multi-scale model of thrombus in arteries

In this article, the time-discretization of the fluid structure interaction model in the three-dimensional boundary domain is taken into account, which explains the mechanical interaction between the blood flow and the Hookean elasticity. The interface between the two phases is given by a soft transition layer and spreads to the finite thickness. On the implicit Euler scheme for this discretization, We derive a variety of priori estimates and then use the Faedo-Galerkin method to prove the local well-poseedness results.