On the absence of "splash" singularities in the case of two-fluid interfaces

Abstract

We show that "splash" singularities cannot develop in the case of locally smooth solutions of the two-fluid interface in two dimensions. More precisely, we show that the scenario of formation of singularities discovered by Castro-Córdoba-Fefferman-Gancedo-Gómez-Serrano in the case of the water waves system, in which the interface remains locally smooth but self-intersects in finite time, is completely prevented in the case of two-fluid interfaces with positive densities.

arXiv commentReplaced the file to correct misprints

References in corpus (5)

• On the Water Waves Equations with Surface Tension
• Global well-posedness of the 3-D full water wave problem
• On the finite-time splash and splat singularities for the 3-D free-surface Euler equations
• Absence of splash singularities for SQG sharp fronts and the Muskat problem
• Finite time singularities for water waves with surface tension

Cited by in corpus (9)

• Global Well-posedness of Free Interface Problems for the incompressible Inviscid Resistive MHD
• Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension
• Large Time Decay Estimates for the Muskat Equation
• Recent advances on the global regularity for irrotational water waves
• Hydrodynamic models and confinement effects by horizontal boundaries
• A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Euler Equation with Surface Tension
• A priori estimates for the free-boundary Euler equations with surface tension in three dimensions
• Regularity results for viscous 3D Boussinesq temperature fronts
• A priori estimates and a blow-up criterion for the incompressible ideal MHD equations with surface tension and a closed free surface