Abstract
AbstractWe analyze the behavior of weak solutions to compressible viscous fluid flows in a bounded domain in$${{\,\mathrm{{\mathbb {R}}}\,}}^3$$R3, randomly perforated by tiny balls with random size. Assuming the radii of the balls scale like$$\varepsilon ^\alpha $$εα,$$\alpha > 3$$α>3, with$$\varepsilon $$εdenoting the average distance between the balls, the problem homogenize to the same limiting equation. Our main contribution is a construction of the Bogovskiĭ operator, uniformly in$$\varepsilon $$ε, without any assumptions on the minimal distance between the balls.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Mechanical Engineering,Mathematics (miscellaneous),Analysis
Cited by
3 articles.
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