2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116577We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interface in $H^{\frac32k +1}$ and the velocity fields in $H^{\frac32k}$. These estimates are obtained using geometric considerations which show that the Kelvin-Helmholtz instabilities are a consequence of a curvature calculation.17 pages, submitted, added referencesAnalysis of PDEsDifferential Geometrytext