In this paper consider a 2-D free boundary Oldroyd-B model at infinite Weissenberg number, under the assumption that the Piola-Kirchoff tensor, entering in the description of the extra-stress tensor, is given by a quadratic, convex energy functional. Our main goal is to investigate the existence of splash type singularities, namely points of self-intersection of the free boundary. The analysis of this problem requires to map the equations via a conformal transformation, in order to separate the singular points, and then to fix the free boundary via a Lagrangian change of coordinates. The investigation starts by proving local existence and stability results for a family of smooth initial configurations which, by considering a special class of initial data, allow us to show the existence of solutions having a self-intersecting configuration. As a consequence of this fact, we can conclude there exists a configuration, which has a singularity of splash type.

Splash singularities for a 2D Oldroyd-B model with nonlinear Piola-Kirchhoff stress

Marcati, Pierangelo;
2017-01-01

Abstract

In this paper consider a 2-D free boundary Oldroyd-B model at infinite Weissenberg number, under the assumption that the Piola-Kirchoff tensor, entering in the description of the extra-stress tensor, is given by a quadratic, convex energy functional. Our main goal is to investigate the existence of splash type singularities, namely points of self-intersection of the free boundary. The analysis of this problem requires to map the equations via a conformal transformation, in order to separate the singular points, and then to fix the free boundary via a Lagrangian change of coordinates. The investigation starts by proving local existence and stability results for a family of smooth initial configurations which, by considering a special class of initial data, allow us to show the existence of solutions having a self-intersecting configuration. As a consequence of this fact, we can conclude there exists a configuration, which has a singularity of splash type.
2017
Existence and stability; Oldroyd-B; Splash singularity; Viscoelasticity; Analysis; Applied Mathematics
File in questo prodotto:
File Dimensione Formato  
2017_NonlinearDifferEquAppl_24_DiIorio.pdf

non disponibili

Tipologia: Altro materiale allegato
Licenza: Non pubblico
Dimensione 413.14 kB
Formato Adobe PDF
413.14 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/20.500.12571/503
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact