Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials

Bogdan–Vasile Matioc, Georg Prokert
2020 Proceedings of the Royal Society of Edinburgh. Section A Mathematics  
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.
doi:10.1017/prm.2020.82 fatcat:54xuzqthjfhgbm6oxyc5b37gna