The inverse of the divergence operator on perforated domains with applications to homogenization problems for the compressible Navier-Stokes system

Abstract

We study the inverse of the divergence operator on a domain \Omega\in R3 perforated by a system of tiny holes. We show that such inverse can be constructed on the Lebesgue space Lp(\Omega) for any 1 < p < 3, with a norm independent of perforation, provided the holes are suitably small and their mutual distance suitably large.

Applications are given to problems arising in homogenization of steady compressible fluid flows.

Keywords

• inverse
• divergence
• operator
• perforated
• domains
• with
• applications
• homogenization
• problems
• for
• compressible
• Navier-Stokes
• system