A phase field $\alpha$-Navier-Stokes vesicle-fluid interaction model: Existence and uniqueness of solutions

Abstract

In this work we analyze a system of nonlinear evolution partial differential equations modeling the fluid-structure interaction associated to the dynamics of an elastic vesicle immersed in a moving incompressible viscous fluid.This system of equations couples an equation for a phase field variable, used to determine the position ofvesicle membrane deformed by the action of the fluid, to the $\alpha$-Navier- Stokes equations with an extra nonlinear interaction term.We prove global in time existence and uniqueness of solutions for this system in suitable functional spaces even in the three-dimensional case.