Inverse of divergence and homogenization of compressible Navier-Stokes equations in randomly perforated domains

Homogenization of a non-linear strongly coupled model of magnetorheological fluids

“…A construction based on Bogovskiȋ map allows us to control the norm of pressure p ε uniformly with respect to ε, c.f. [1,2,5,18,20,21,41].…”

Homogenization of the full compressible Navier-Stokes-Fourier system in randomly perforated domains

“…To pass to the limit in the momentum equation, we need to construct suitable test functions. To this end, we recall a lemma from [5]: Lemma 5.1. Let α > 2, D ⊂ R 3 be a bounded C 2 domain with 0 ∈ D, and (Φ, R) = ({z i }, {r i }) be a marked Poisson point process with intensity λ > 0 and r i ≥ 0 with E(r mr i ) < ∞ for m r > max{3/(α − 2), 3}.…”

“…The case of small particles (α > 3) was treated in [9,11,18] for different growing conditions on the pressure. Random perforations in the spirit of [15] for small particles were considered by Bella and the author in [5], where in the limit, the equations remain unchanged as in the periodic case.…”

“…The key point is to develop uniform bounds for B ε as ε → 0. In the case of periodically perforated domains with deterministic radii ε α , α ≥ 1, this was done in [9,11,18] and recently generalized to the case of random distributions, random radii and α > 2 in [5]. We will use this Bogovskiȋ operator for the random case in order to generalize the results of [17].…”

Homogenization and low Mach number limit of compressible Navier-Stokes equations in critically perforated domains

“…The case of small particles (α > 3) was treated in [6,7,15] for different growing conditions on the pressure. Random perforations in the spirit of [12] for small particles were considered by the authors in [4], where in the limit, the equations remain unchanged as in the periodic case.…”