In this paper we consider the Navier–Stokes–Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. Incontrast with previous results regarding this system, vacuum regions are allowed in the definition of weak solutions and no additional damping terms are considered. The compactness is obtained by introducing suitable truncations of the velocity field and the mass density at different scales and use only the a priori bounds obtained by the energy and the BD entropy.

On the compactness of weak solutions to the Navier-Stokes-Korteweg equations for capillary fluids

Antonelli P;
2019

Abstract

In this paper we consider the Navier–Stokes–Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove compactness of finite energy weak solutions for large initial data. Incontrast with previous results regarding this system, vacuum regions are allowed in the definition of weak solutions and no additional damping terms are considered. The compactness is obtained by introducing suitable truncations of the velocity field and the mass density at different scales and use only the a priori bounds obtained by the energy and the BD entropy.
Compressible fluids, Navier–Stokes–Korteweg, Capillarity, Vacuum, Compactness
File in questo prodotto:
File Dimensione Formato  
PostPrint_2019_NonlinearAnal_Theor_87_Antonelli.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 239.16 kB
Formato Adobe PDF
239.16 kB Adobe PDF Visualizza/Apri

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/20.500.12571/1858
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 11
social impact