Abstract

MORALES, Fernando A.. The asymptotic analysis of a Darcy-Stokes system coupled through a curved interface. Integración - UIS [online]. 2019, vol.37, n.2, pp.261-297.  Epub Oct 10, 2019. ISSN 0120-419X.  https://doi.org/10.18273/revint.v37n2-2019004.

We present the asymptotic analysis of a Darcy-Stokes coupled system, modeling the fluid exchange between a narrow channel (Stokes flow) and a porous medium (Darcy flow), coupled through a C2 curved interface. The channel is a cylindrical domain between the interface (Γ) and a parallel translation of itself The introduction of a change variable (to fix the domain geometry) and the introduction of two systems of coordinates: the Cartesian and a local one (consistent with the geometry of the surface), permit to find the limiting form of the system when the width of the channel tends to zero (є → 0). The limit problem is a coupled system with Darcy flow in the porous medium and Brinkman flow on the curved interface (Γ).

MSC2010: 35K50, 35B25, 80A20, 35F15.

Keywords : porous media; curved interfaces; Darcy-Stokes system; Darcy-Brinkman system.

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