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arXiv · 2501.09195

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

Tim Binz·Matthias Hieber·Arnab Roy
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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.

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Tim Binz, Matthias Hieber, Arnab Roy. 2025-01-15. Fluid-Structure Interaction with Porous Media: The Beaver-Joseph condition in the strong sense. https://arxiv.org/abs/2501.09195

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