论文标题
两阶段Stokes在完整的2D空间中按毛细管流动：通过流体动力电位的方法
Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials
论文作者
论文摘要
我们研究了由表面张力驱动的两相Stokes流，其粘度相等的流体驱动，并由图几何形状渐近平坦的界面隔开。假定流量为流体填充整个空间是二维的。我们在Sobolev空间中证明了适合的和抛物线的平滑性，直至至关重要。主要技术工具是对非线性单数积分算子的分析，该算子是由流体动力的单层潜力和非线性抛物线进化方程的抽象结果分析。
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.
