AI 中文总结
研究穿孔区域中非均匀不可压缩导热流体均匀化，其粘度和热传导系数与温度有关，孔洞直径为\(\varepsilon^{\alpha} \ (\alpha>3)\)，证明\(\varepsilon\to 0\)时速度、密度和温度极限行为由无孔均匀区域原始系统决定。
AI 中文摘要
本文研究了具有亚临界尺寸孔洞的穿孔区域中三维非均匀不可压缩导热流体的均匀化问题，其中粘度和热传导系数假定依赖于温度。孔洞直径为\(\varepsilon^{\alpha} \ (\alpha>3)\)，\(\varepsilon > 0\)是衡量孔洞间距的小参数。我们证明当\(\varepsilon\to 0\)时，速度、密度和温度的极限行为由无孔洞均匀区域中的原始系统支配。
英文摘要
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 $\varepsilon^α \ (α>3)$, 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.
CommentsHomogenization; perforated domains; non-homogeneous incompressible heat- conducting fluid
