WELL-POSED STOKES/BRINKMAN AND STOKES/DARCY COUPLING REVISITED WITH NEW JUMP INTERFACE CONDITIONS
Résumé
The global well-posedness in time is proved, with no restriction on the size of the data, for the Stokes/Brinkman and Stokes/Darcy coupled flow problems with new jump interface conditions recently derived in [11] by asymptotic modelling and shown to be physically relevant. These original conditions include jumps of both stress and tangential velocity vectors at the fluid-porous interface. They can be viewed as generalizations for the multi-dimensional flow of Beavers & Joseph's jump condition of tangential velocity and Ochoa-Tapia & Whitaker's jump condition of shear stress. Therefore, they are different from those most commonly used in the literature. The case of Saffman's approximation is also studied, but with a force balance for the cross-flow including the Darcy drag and inducing a law of pressure jump different from the usual one. The proof of these results follows the general framework briefly introduced in [7, 8] for the steady flow.
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