Asymptotic behavior of the Stokes problem with Robin condition in a domain with small holes
Chafia Karek, Amar Ould-Hammouda · Asymptotic Analysis · 2019
We consider the Stokes problem in a domain [Formula: see text] of [Formula: see text], [Formula: see text] ε-periodically perforated by holes of size [Formula: see text] and [Formula: see text] ( ε, [Formula: see text], [Formula: see text] being small parameters), with [Formula: see text] and [Formula: see text] as [Formula: see text]. Our aim is to describe the asymptotic behavior of the velocity and the pressure of the fluid as [Formula: see text] and give, if possible, a limit (“homogenized”) problem. To do so, we use the periodic unfolding method introduced by Cioranescu, Damlamian and Griso ( C. R. Acad. Sci. Paris, Ser. I 335 ( 2002 ) 99–104; SIAM J. of Math. Anal. 40(4) ( 2008 ) 1585–1620). It allow us to consider a general geometric framework and so, to extend the results from Cioranescu, Donato and Ene ( Math. Models and Methods in Appl. Sciences 19 ( 1996 ) 857–881) and Capatina and Ene ( European J. of Math. 22 ( 2011 ) 333–345).