Local well-posedness and non-collapsing of interfacial Stokes flow with bending forces on mean convex hypersurfaces

The earlier well-posedness of interfacial viscous Stokes flow in two and three dimensions was extensively studied. In this paper, well-posedness results will be generalized to cases with bending forces involved, on the mean convex hypersurfaces. The main techniques used in this paper, are utilizing the Poincaré residue to calculate the principal value of the Green’s function on the hypersurface, and using monotonic quantities to extract the leading order. Then use the prior estimates to bound the lower-order nonlinear terms.