Fluid-poroviscoelastic structure interaction problem with nonlinear geometric coupling

TL;DR

This paper proves the existence of weak solutions for a complex fluid-poroviscoelastic interaction problem with nonlinear geometric coupling, advancing mathematical understanding of such coupled systems.

Contribution

It provides the first weak solution existence proof for an FSI problem involving nonlinear coupling with a Biot poroviscoelastic medium.

Findings

Existence of weak solutions for the regularized problem.

Convergence of weak solutions to classical solutions under regularity assumptions.

Extension from poroelastic to poroviscoelastic media.

Abstract

We investigate weak solutions to a fluid-structure interaction (FSI) problem between the flow of an incompressible, viscous fluid modeled by the Navier-Stokes equations, and a poroviscoelastic medium modeled by the Biot equations. These systems are coupled nonlinearly across an interface with mass and elastic energy, modeled by a reticular plate equation, which is transparent to fluid flow. We provide a constructive proof of the existence of a weak solution to a regularized problem. Next, a weak-classical consistency result is obtained, showing that the weak solution to the regularized problem converges, as the regularization parameter approaches zero, to a {{classical}} solution to the original problem, when such a classicalsolution exists. While the assumptions in the first step only require the Biot medium to be poroelastic, the second step requires additional regularity, namely, that the Biot medium is poroviscoelastic. This is the first weak solution existence result for an FSI problem with nonlinear coupling involving a Biot model for poro(visco)elastic media.