Inverse of divergence and homogenization of compressible Navier-Stokes equations in randomly perforated domains
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Date
2023-02-24
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Abstract
We analyze the behavior of weak solutions to compressible viscous fluid flows in a bounded domain in R3, randomly perforated by tiny balls with random size. Assuming the radii of the balls scale like εα, α > 3, with ε denoting the average
distance between the balls, the problem homogenize to the same limiting equation. Our main contribution is a construction of the Bogovski˘ı operator, uniformly in ε, without any assumptions on the minimal distance between the balls.
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Navier-Stokes-Gleichung, Fluiddynamik, Homogenisierung <Mathematik>, Divergenz <Vektoranalysis>, Kompressibilität