带有极小孔洞区域中松弛可压缩粘性两相流体模型的均质化
Homogenization of a relaxed compressible viscous two-phase fluid model in a domain with very tiny holes
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中文总结 AI 辅助
该研究针对带极小孔洞区域的可压缩Navier-Stokes-Korteweg近似系统，证明当障碍物尺寸远快于间距趋于零时极限系统不变，扩展了单相可压缩Navier-Stokes方程的均质化结果至两相流体情形。
中文摘要 AI 辅助
我们研究有界区域内被小障碍物周期性穿孔的可压缩Navier-Stokes-Korteweg方程的近似系统。当障碍物尺寸比其间距更快地趋于零时，我们在二维和三维空间中证明极限系统保持不变。该结果适用于一大类单调和非单调压力函数，尤其在物理相关情形下成立，此时该近似系统用于描述可压缩粘性两相流体的动力学，扩展了单相可压缩Navier-Stokes方程对应的已知均质化结果。
英文摘要
We study an approximate system for the compressible Navier-Stokes-Korteweg equations in a bounded domain periodically perforated by small obstacles. As the size of the obstacles decrease much faster to zero than their mutual distances, we show in spatial dimension two and three that the limiting system remains unchanged. Our result applies for a large class of monotone and non-monotone pressure functions. In particular, it holds in the physically relevant case when the approximate system is used to describe the dynamics of a compressible viscous two-phase fluid extending the corresponding homogenization results known for the compressible Navier-Stokes equations in a single-phase setting.
