2015/05/08 by Coutand, Daniel, Shkoller, Steve · 1 citation
#35Q30 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1505.01929
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. We prove that for d-dimensional flows, d=2 or 3, the free-surface of a viscous water wave, modeled by the incompressible Navier-Stokes equations with moving free-boundary, has a finite-time splash singularity. In particular, we prove that given a sufficiently smooth initial boundary and divergence-free velocity field, the interface will self-intersect in finite time.