Homogenization of a non-homogeneous incompressible heat-conducting fluid in perforated domains

Yong Lu; Jiaojiao Pan; Luqi Wang

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arXiv · 2607.11036

Homogenization of a non-homogeneous incompressible heat-conducting fluid in perforated domains

Yong Lu·Jiaojiao Pan·Luqi Wang

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Abstract

This paper provides the study of the homogenization of the 3D non-homogeneous incompressible heat-conducting fluid in perforated domains with holes of subcritical size, where the viscosity and the heat conductivity coefficient are assumed to depend on the temperature. The diameter of the holes is of order $\varepsilon^{\alpha} \ (\alpha>3)$, where $\varepsilon > 0$ is a small parameter that measures the mutual distance between the holes. We prove that as $\varepsilon\to 0$, the limit behavior of velocity, density and temperature is governed by the original system in homogeneous domain without holes.

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Yong Lu, Jiaojiao Pan, Luqi Wang. 2026-07-13. Homogenization of a non-homogeneous incompressible heat-conducting fluid in perforated domains. https://arxiv.org/abs/2607.11036

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