Fluid-Structure Interaction with Porous Media: The Beaver-Joseph condition in the strong sense

TL;DR

This paper investigates fluid-structure interaction involving porous media using Navier-Stokes equations and the Beaver-Joseph interface condition, establishing existence, uniqueness, and regularity of solutions in a novel strong sense.

Contribution

It introduces the first analysis of the Beaver-Joseph condition in the strong sense, proving global strong solutions and regularity results for the coupled system.

Findings

Unique, global strong solutions exist under small data.

A Serrin-type blow-up criterion is established.

Solutions are analytic if forces are sufficiently regular.

Abstract

This article considers fluid structure interaction describing the motion of a fluid contained in a porous medium. The fluid is modelled by Navier-Stokes equations and the coupling between fluid and the porous medium is described by the classical Beaver-Joseph or the Beaver-Joseph-Saffman interface condition. In contrast to previous work these conditions are investigated for the first time in the strong sense and it is shown that the coupled system admits a unique, global strong solution in critical spaces provided the data are small enough. Furthermore, a Serrin-type blow-up criterium is developed and higher regularity estimates at the interface are established, which say that the solution is even analytic provided the forces are so.