标题： 一种势论方法用于毛细管驱动的Hele-Shaw问题 显示英文标题

标题： A potential theory approach to the capillarity-driven Hele-Shaw problem

摘要： 在本文中，我们证明了势论为分析有限几何中的准稳态流体流动提供了一个强大的框架，其中整体动力学由具有常系数的椭圆方程控制。 这种方法通过二维Hele-Shaw问题与表面张力进行了说明，我们推导出了在（几乎）最优函数空间中的局部适定性和抛物线平滑性。 此外，我们建立了一个抽象拟线性抛物问题特定类别的线性化稳定性广义原理，这使我们能够证明Hele-Shaw问题的平稳解是指数稳定的。 显示英文摘要

摘要： In this paper, we demonstrate that potential theory provides a powerful framework for analyzing quasistationary fluid flows in bounded geometries, where the bulk dynamics are governed by elliptic equations with constant coefficients. This approach is illustrated by the two-dimensional Hele-Shaw problem with surface tension, for which we derive local well-posedness and parabolic smoothing in (almost) optimal function spaces. In addition, we establish a generalized principle of linearized stability for a particular class of abstract quasilinear parabolic problems, which enables us to show that the stationary solutions to the Hele-Shaw problem are exponentially stable.