Inverse of Divergence and Homogenization of Compressible Navier–Stokes Equations in Randomly Perforated Domains
Peter Bella, Florian Oschmann · Archive for Rational Mechanics and Analysis · 2023
Abstract We 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 $$\varepsilon $$ ε denoting 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.