Quantitative homogenization theory for random suspensions in steady Stokes flow
Quantitative homogenization theory for random suspensions in steady Stokes flow
复制标题
稳定斯托克斯流中随机悬浮体的定量均质化理论
DOI：
10.5802/jep.204
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
A. Gloria
中科院分区：
文献类型：
--
作者：
Mitia Duerinckx;A. Gloria
摘要。本工作发展了稳定斯托克斯流中刚性颗粒随机悬浮的定量均匀化理论，并完成了最近的定性结果。更准确地说，我们建立了Stokes问题的大尺度正则性理论，并证明了相关校正量的矩界和均匀化误差的最优估计；后者进一步要求对随机悬架进行定量遍历假设。与发散型线性椭圆方程的定量均匀化理论相比，对流体不可压缩性和粒子刚性约束的分析存在很大的困难。我们的分析进一步适用于（可压缩或不可压缩）线弹性和静电中的刚性内含物问题；在这些情况下，即使在周期性设置中，它也是新的。
Abstract. This work develops a quantitative homogenization theory for random suspensions of rigid particles in a steady Stokes flow, and completes recent qualitative results. More precisely, we establish a large-scale regularity theory for this Stokes problem, and we prove moment bounds for the associated correctors and optimal estimates on the homogenization error; the latter further requires a quantitative ergodicity assumption on the random suspension. Compared to the corresponding quantitative homogenization theory for divergence-form linear elliptic equations, substantial difficulties arise from the analysis of the fluid incompressibility and the particle rigidity constraints. Our analysis further applies to the problem of stiff inclusions in (compressible or incompressible) linear elasticity and in electrostatics; it is also new in those cases, even in the periodic setting.