Variational methods for fluid-structure interaction and porous media

TL;DR

This paper develops a variational framework to prove the existence of weak solutions for coupled fluid-poroelastic solid systems involving large deformations, inertia, and non-convex functionals in incompressible fluid flows.

Contribution

It introduces a novel variational approach to establish existence results for complex fluid-structure interaction models with large deformations and inertia.

Findings

Existence of weak solutions for coupled fluid-poroelastic systems.

Handling large deformations and inertia in a variational framework.

Application to incompressible Navier-Stokes driven flows.

Abstract

In this work we consider a poroelastic flexible material that may deform largely which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three space dimensions. By a variational approach we show existence of weak solutions for a class of such coupled systems. We consider the unsteady case, this means that the PDE for the poroelastic solid involves the Frechet derivative of a non-convex functional as well as (second order in time) inertia terms.