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Generalized Darcy-Oseen resolvent problem. (English) Zbl 1339.35247
Summary: 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.
35Q35 PDEs in connection with fluid mechanics
76S05 Flows in porous media; filtration; seepage
76D07 Stokes and related (Oseen, etc.) flows
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76Z05 Physiological flows
Full Text: DOI
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