Splash singularity for a free-boundary incompressible viscoelastic fluid model

TL;DR

This paper proves the existence of splash singularities in a 2D free-boundary viscoelastic fluid model of Oldroyd-B type at infinite Weissenberg number, showing boundary self-intersection while remaining smooth.

Contribution

It extends previous Navier-Stokes splash singularity results to a viscoelastic fluid model using conformal mapping and Lagrangian methods.

Findings

Existence of splash singularities in the viscoelastic model.

Construction of initial data evolving into self-intersecting boundaries.

Extension of Navier-Stokes splash results to viscoelastic fluids.

Abstract

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).