Homogenization of the Full Compressible Navier-Stokes-Fourier System in Randomly Perforated Domains

Abstract

We consider the homogenization of the compressible Navier-Stokes-Fourier equations in a randomly perforated domain in $${\mathbb {R}}^3$$ R 3 . Assuming that the particle size scales like $$\varepsilon ^\alpha $$ ε α , where $$\varepsilon >0$$ ε > 0 is their mutual distance and $$\alpha >3$$ α > 3 , we show that in the limit $$\varepsilon \rightarrow 0$$ ε → 0 , the velocity, density, and temperature converge to a solution of the same system. We follow the methods of Lu and Pokorný [https://doi.org/10.1016/j.jde.2020.10.032] and Pokorný and Skříšovský [https://doi.org/10.1007/s41808-021-00124-x] where they considered the full system in periodically perforated domains.

Homogenization of the Navier–Stokes equations in perforated domains in the inviscid limit

“…[HLW22,LLN18,LM16a,MP99]) to compressible viscous flows (see e.g. [BO23,HKS21,Mas02,Osc22]) and even non-Newtonian fluids (see e.g. [Mik18]) have been considered with different boundary conditions, including Navier slip conditions (see e.g.…”