标题： 斯托克斯方程与紧密排列刚性夹杂物的最优高阶导数估计 显示英文标题

标题： Optimal higher derivative estimates for Stokes equations with closely spaced rigid inclusions

摘要： 在本文中，我们研究了悬浮在斯托克斯流中的两个紧密排列的刚性夹杂物之间的相互作用。众所周知，当夹杂物之间的距离趋近于零时，夹杂物之间的狭窄区域中的应力会显著放大。为了更深入地了解这些相互作用，我们在二维情况下存在两个刚性夹杂物的情况下，推导了斯托克斯方程的高阶导数估计。我们的方法与处理标准凸积分方案中不可压缩性约束的方法相呼应。在对域进行某些对称性假设的情况下，这些估计被证明是最佳的。因此，我们建立了狭窄区域内柯西应力及其高阶导数的精确爆破速率。 显示英文摘要

摘要： In this paper, we study the interaction between two closely spaced rigid inclusions suspended in a Stokes flow. It is well known that the stress significantly amplifies in the narrow region between the inclusions as the distance between them approaches zero. To gain deeper insight into these interactions, we derive high-order derivative estimates for the Stokes equation in the presence of two rigid inclusions in two dimensions. Our approach resonates with the method used to handle the incompressibility constraint in the standard convex integration scheme. Under certain symmetric assumptions on the domain, these estimates are shown to be optimal. As a result, we establish the precise blow-up rates of the Cauchy stress and its higher-order derivatives in the narrow region.