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In this paper, one considers the coupling of a Brinkman model and Stokesequations with jump embedded transmission conditions. In this model, oneassumes that the viscosity in the porous region is very small. Then we derive aWentzel--Kramers--Brillouin (WKB) expansion in power series of the square rootof this small parameter for the velocity and the pressure which are solution ofthe transmission problem. This WKB expansion is justified rigorously by provinguniform errors estimates.

Asymptotic Study for Stokes-Brinkman model with jump embedded transmission conditions