The two-phase quasi-stationary Stokes flow by capillarity in the plane

Abstract: We discuss a two-phase moving boundary problem that describes the two-dimensional quasistationary Stokes flow of two fluids with different densities and viscosities that occupy the entire plane in the regime where surface tension effects are taken into account at the interface that separates the fluids. In this setting the classical methods of potential theory can be used to transform the model into a nonlinear and nonlocal evolution problem for the function that parameterizes the interface between the fluids, the nonlinearities being expressed by singular integral operators. This problem is of parabolic type, well-posed in all Sobolev spaces up to critical regularity, and it features some parabolic smoothing properties. Joint work with Georg Prokert.

analysis of PDEs

Audience: researchers in the topic

PDE seminar via Zoom