We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire space. We prove well-posedness and parabolic smoothing in Sobolev spaces up to critical regularity. The main technical tools are an analysis of nonlinear singular integral operators arising from the hydrodynamic single-layer potential and abstract results on nonlinear parabolic evolution equations.

中文翻译：

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在全二维空间中通过毛细作用进行两相斯托克斯流动：一种通过流体动力势的方法

我们研究了由表面张力驱动的两相斯托克斯流，两种流体具有相同的粘度，由具有图形几何的渐近平面界面隔开。假设流动是二维的，流体充满整个空间。我们证明了 Sobolev 空间中的适定性和抛物线平滑达到临界规律。主要的技术工具是对由水动力单层势产生的非线性奇异积分算子的分析和非线性抛物演化方程的抽象结果。