  We consider a system of two incompressible fluids separated by a free
interface. The first fluid is inviscid, governed by the Euler system, while the
second fluid has positive viscosity and is governed by the Navier-Stokes
system. We formulate a notion of splash-type self-intersection singularities,
and show that this system cannot form such a singularity in finite time. The
main obstacle in our analysis is to handle the effect of bulk vorticity induced
by the Navier-Stokes flow. To the best of our knowledge this is the first
result on preclusion of splash-type singularities in the presence of
non-trivial vorticity interior to one of the fluids.
