# Analysis of the coupled Navier-Stokes/Biot problem

## TL;DR

This paper investigates a complex coupled fluid-structure interaction model involving Navier-Stokes and Biot equations, establishing mathematical existence, uniqueness, and stability results under small data conditions.

## Contribution

It provides the first rigorous analysis of the fully dynamic coupled Navier-Stokes/Biot problem, including existence, uniqueness, and a priori estimates.

## Key findings

- Existence and uniqueness of solutions under small data assumptions.
- Derivation of a priori estimates for the coupled system.
- Mathematical framework for analyzing fluid-poroelastic interactions.

## Abstract

We analyze a weak formulation of the coupled problem defining the interac- tion between a free fluid and a poroelastic structure. The problem is fully dynamic and is governed by the time-dependent incompressible Navier-Stokes equations and the Biot equations. Under a small data assumption, existence and uniqueness results are proved and a priori estimates are provided.