Fluid-structure interaction with porous media: The Beaver-Joseph condition in the strong sense

This article considers fluid structure interaction describing the motion of a fluid contained in a porous medium. The fluid is modeled 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. (c) 2025 Published by Elsevier Inc.