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In this paper we highlight a set of ad hoc test functions to study thehomogenization of viscous compressible fluid in domains with tiny holes. Thisset of functions allows to improve previous results in dimensions two andthree. As an application we show that the presence of a small obstacle does notinfluence the dynamics of a viscous compressible fluid in dimension two.

Ad hoc test functions for homogenization of compressible viscous fluid with application to the obstacle problem in dimension two