Splash singularities for the free boundary Navier-Stokes equations

TL;DR

This paper demonstrates that smooth initial conditions in 2D free boundary Navier-Stokes equations can lead to finite-time interface breakdown into a splash singularity, highlighting complex fluid interface dynamics.

Contribution

It establishes the existence of initial data leading to splash singularities in 2D free boundary Navier-Stokes equations, a novel result in fluid dynamics.

Findings

Finite-time formation of splash singularities from smooth initial data

Existence proof for initial conditions causing interface breakdown

Insights into fluid interface instability mechanisms

Abstract

In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Navier-Stokes equations, for which the smoothness of the interface breaks down in finite time into a splash singularity.