Generalized Darcy–Oseen resolvent problem |
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| Authors: | Dagmar Medková Mariya Ptashnyk Werner Varnhorn |
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| Institution: | 1. Mathematical Institute of the Academy of Sciences of the Czech Republic, Praha 1, Czech Republic;2. Division of Mathematics, University of Dundee, Dundee, Scotland, UK;3. Institute of Mathematics, University of Kassel, Kassel, Germany |
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| Abstract: | In this paper, we study the well‐posedness of a coupled Darcy–Oseen resolvent problem, describing the fluid flow between free‐fluid domains and porous media separated by a semipermeable membrane. The influence of osmotic effects, induced by the presence of a semipermeable membrane, on the flow velocity is reflected in the transmission conditions on the surface between the free‐fluid domain and the porous medium. To prove the existence of a weak solution of the generalized Darcy–Oseen resolvent system, we consider two auxiliary problems: a mixed Navier–Dirichlet problem for the generalized Oseen resolvent system and Robin problem for an elliptic equation related to the general Darcy equations. © 2016 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons Ltd. |
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| Keywords: | Darcy– Oseen resolvent problem semipermeable membrane Brinkman– Darcy equations fluid flow between free‐fluid domains and porous media compact perturbations |
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