In this paper we study how to approximate the Leray weak solutions of the incompressible Navier-Stokes equations. In particular we describe an hyperbolic version of the so-called artificial compressibility method investigated by J. L. Lions and Temam. By exploiting the wave equation structure of the pressure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimates of Strichartz type. We prove that the projection of the approximating velocity fields on the divergence free vectors is relatively compact and converges to a Leray weak solution of the incompressible Navier-Stokes equation. © 2006 World Scientific Publishing Company.

A Dispersive approach to the artificial compressibility approximations of the Navier-Strokes equations in 3D

MARCATI, PIERANGELO
2006

Abstract

In this paper we study how to approximate the Leray weak solutions of the incompressible Navier-Stokes equations. In particular we describe an hyperbolic version of the so-called artificial compressibility method investigated by J. L. Lions and Temam. By exploiting the wave equation structure of the pressure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimates of Strichartz type. We prove that the projection of the approximating velocity fields on the divergence free vectors is relatively compact and converges to a Leray weak solution of the incompressible Navier-Stokes equation. © 2006 World Scientific Publishing Company.
Hyperbolic equations; Incompressible Navier-Stokes equation; Wave equations; Mathematics (all); Analysis
File in questo prodotto:
File Dimensione Formato  
2006_JHyperbolicDifferEqu_3_Donatelli_Marcati.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Accesso gratuito
Dimensione 260.45 kB
Formato Adobe PDF
260.45 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/20.500.12571/2199
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 19
  • ???jsp.display-item.citation.isi??? 20
social impact