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Explore the mathematical analysis of fluid droplet evolution in vacuum through this 26-minute conference lecture examining the equilibrium between surface tension and fluid forces at free boundaries. Delve into higher-order energy estimates for the planar case of incompressible quasi-steady Stokes equations, focusing on bounds for curvature and tangential derivatives alongside second and third spatial derivatives of fluid velocity. Learn about quantitative bounds that depend solely on initial geometry properties and remain valid until topological degeneracy occurs. Discover how this Eulerian approach differs from traditional local coordinate methods by providing geometrically intrinsic estimates that maintain validity until these intrinsic qualities break down. Understand the collaborative research findings with Malte Kampschulte and Joonas Niinikoski that advance the mathematical understanding of free boundary problems in fluid dynamics.
