  In this paper we analyze a 2D free-boundary viscoelastic fluid model of
Oldroyd-B type at infinite Weissenberg number. Our main goal is to show the
existence of the so-called splash singularities, namely points where the
boundary remains smooth but self-intersects. The combination of existence and
stability results allows us to construct a special class of initial data, which
evolve in time into self-intersecting configurations. To this purpose we apply
the classical conformal mapping method and later we move to the Lagrangian
framework, as a consequence we deduce the existence of splash singularities.
This result extends the result obtained for the Navier-Stokes equations in
"Splash singularities for the free-boundary Navier-Stokes" by Castro, A. et al.
(2015).
