The vanishing viscosity limit in the presence of a porous medium

Christophe Lacave, Anna L. Mazzucato

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and distance, and of vanishing viscosity. Under suitable conditions on the particle size, particle distance, and viscosity, we prove that solutions of the Navier–Stokes system in the perforated domain converges to solutions of the Euler system, modeling inviscid, incompressible flow, in the full plane. That is, the flow is not disturbed by the porous medium and becomes inviscid in the limit. Convergence is obtained in the energy norm with explicit rates of convergence.

Original languageEnglish (US)
Pages (from-to)1527-1557
Number of pages31
JournalMathematische Annalen
Volume365
Issue number3-4
DOIs
StatePublished - Aug 1 2016

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Perforated Domains
Vanishing Viscosity
Particle Size
Porous Media
Euler System
Navier-Stokes System
Newtonian Fluid
Incompressible Flow
System Modeling
Viscosity
Rate of Convergence
Converge
Norm
Energy

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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The vanishing viscosity limit in the presence of a porous medium. / Lacave, Christophe; Mazzucato, Anna L.

In: Mathematische Annalen, Vol. 365, No. 3-4, 01.08.2016, p. 1527-1557.

Research output: Contribution to journalArticle

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