Global existence of weak solutions to a nonlocal Cahn-Hilliard-Navier-Stokes system (Articolo in rivista)

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Label
  • Global existence of weak solutions to a nonlocal Cahn-Hilliard-Navier-Stokes system (Articolo in rivista) (literal)
Anno
  • 2012-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1016/j.jmaa.2011.08.008 (literal)
Alternative label
  • Pierluigi Colli; Sergio Frigeri; Maurizio Grasselli (2012)
    Global existence of weak solutions to a nonlocal Cahn-Hilliard-Navier-Stokes system
    in Journal of mathematical analysis and applications (Print); Elsevier Inc., San Diego (Stati Uniti d'America)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Pierluigi Colli; Sergio Frigeri; Maurizio Grasselli (literal)
Pagina inizio
  • 428 (literal)
Pagina fine
  • 444 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://www.sciencedirect.com/science/article/pii/S0022247X1100744X# (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 386 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 1 (literal)
Note
  • Scopu (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Dipartimento di Matematica F. Casorati, Università degli Studi di Pavia, Pavia I-27100, Italy; Dipartimento di Matematica F. Enriques, Università degli Studi di Milano, Milano I-20133, Italy; Dipartimento di Matematica F. Brioschi, Politecnico di Milano, Milano I-20133, Italy (literal)
Titolo
  • Global existence of weak solutions to a nonlocal Cahn-Hilliard-Navier-Stokes system (literal)
Abstract
  • A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary fluids and it has been investigated by many authors. Here we consider a variant of this model where the standard Cahn-Hilliard equation is replaced by its nonlocal version. More precisely, the gradient term in the free energy functional is replaced by a spatial convolution operator acting on the order parameter ?, while the potential F may have any polynomial growth. Therefore the coupling with the Navier-Stokes equations is difficult to handle even in two spatial dimensions because of the lack of regularity of ?. We establish the global existence of a weak solution. In the two-dimensional case we also prove that such a solution satisfies the energy identity and a dissipative estimate, provided that F fulfills a suitable coercivity condition. (literal)
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