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 [4].

Splash singularity for a free-boundary incompressible viscoelastic fluid model

Marcati P.;Spirito S.
2020-01-01

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 [4].
File in questo prodotto:
File Dimensione Formato  
1806.11089.pdf

Open Access dal 02/03/2020

Descrizione: Author Accepted Manuscript
Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 2.63 MB
Formato Adobe PDF
2.63 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/145991
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 2
social impact