We study the nonlinear almost compressible 2D Oberbeck-Boussinesq system, characterized by an extra buoyancy term where the density depends on the pressure, and a corresponding dimensionless parameter β, proportional to the (positive) compressibility factor β0. The local in time existence of the perturbation to the conductive solution is proved for any "size" of the initial data. However, unlike the classical problem where β0 = 0, a smallness condition on the initial data is needed for global in time existence, along with smallness of the Rayleigh number. Removing this condition appears quite challenging, and we leave it as an open question.

Existence and nonlinear stability of convective solutions for almost compressible fluids in Bénard problem

Passerini A.
2019

Abstract

We study the nonlinear almost compressible 2D Oberbeck-Boussinesq system, characterized by an extra buoyancy term where the density depends on the pressure, and a corresponding dimensionless parameter β, proportional to the (positive) compressibility factor β0. The local in time existence of the perturbation to the conductive solution is proved for any "size" of the initial data. However, unlike the classical problem where β0 = 0, a smallness condition on the initial data is needed for global in time existence, along with smallness of the Rayleigh number. Removing this condition appears quite challenging, and we leave it as an open question.
2019
De Martino, A.; Passerini, A.
File in questo prodotto:
File Dimensione Formato  
JMP19-AR-00578.pdf

accesso aperto

Descrizione: Post print
Tipologia: Post-print
Licenza: PUBBLICO - Pubblico con Copyright
Dimensione 428.57 kB
Formato Adobe PDF
428.57 kB Adobe PDF Visualizza/Apri
1.5102063.pdf

accesso aperto

Descrizione: Full text editoriale
Tipologia: Full text (versione editoriale)
Licenza: PUBBLICO - Pubblico con Copyright
Dimensione 4.55 MB
Formato Adobe PDF
4.55 MB Adobe PDF Visualizza/Apri

I documenti in SFERA 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/11392/2412018
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 7
social impact