An interpretation of Temam’s extra force in the quasi-incompressible Navier–Stokes system

We discuss the role of the extra force densityfe=−12(∇·v)vin the adimensionalized system of partial differential equations{∂v∂t+(v·∇)v+∇p−1ReΔv=f+fe,1K∂p∂t+∇·v=0,K>>1,whose weak solution, with appropriate initial and boundary conditions, has been proved in [Arch. Rat. Mech. Analysis, 32:135–15...

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Autor principal:	Giuseppe Tomassetti
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Inertia Kinetic energy Fluid mechanics Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/986d881b6e674a4aa48d9b2eddacac53
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spelling	oai:doaj.org-article:986d881b6e674a4aa48d9b2eddacac532021-12-01T05:05:47ZAn interpretation of Temam’s extra force in the quasi-incompressible Navier–Stokes system2666-496810.1016/j.apples.2020.100028https://doaj.org/article/986d881b6e674a4aa48d9b2eddacac532021-03-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666496820300285https://doaj.org/toc/2666-4968We discuss the role of the extra force densityfe=−12(∇·v)vin the adimensionalized system of partial differential equations{∂v∂t+(v·∇)v+∇p−1ReΔv=f+fe,1K∂p∂t+∇·v=0,K>>1,whose weak solution, with appropriate initial and boundary conditions, has been proved in [Arch. Rat. Mech. Analysis, 32:135–153] to preserve the balance of energy while approximating, in the limit K→∞, the weak solution of the incompressible Navier-Stokes system, where the extra force vanishes. Taking the cue from [Ann. Mat. Pura Appl. 172:103–124], we provide a mechanical interpretation of the extra force density fe, arguing that it is a manifestation of inertia.Giuseppe TomassettiElsevierarticleInertiaKinetic energyFluid mechanicsEngineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 5, Iss , Pp 100028- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Inertia Kinetic energy Fluid mechanics Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Inertia Kinetic energy Fluid mechanics Engineering (General). Civil engineering (General) TA1-2040 Giuseppe Tomassetti An interpretation of Temam’s extra force in the quasi-incompressible Navier–Stokes system
description	We discuss the role of the extra force densityfe=−12(∇·v)vin the adimensionalized system of partial differential equations{∂v∂t+(v·∇)v+∇p−1ReΔv=f+fe,1K∂p∂t+∇·v=0,K>>1,whose weak solution, with appropriate initial and boundary conditions, has been proved in [Arch. Rat. Mech. Analysis, 32:135–153] to preserve the balance of energy while approximating, in the limit K→∞, the weak solution of the incompressible Navier-Stokes system, where the extra force vanishes. Taking the cue from [Ann. Mat. Pura Appl. 172:103–124], we provide a mechanical interpretation of the extra force density fe, arguing that it is a manifestation of inertia.
format	article
author	Giuseppe Tomassetti
author_facet	Giuseppe Tomassetti
author_sort	Giuseppe Tomassetti
title	An interpretation of Temam’s extra force in the quasi-incompressible Navier–Stokes system
title_short	An interpretation of Temam’s extra force in the quasi-incompressible Navier–Stokes system
title_full	An interpretation of Temam’s extra force in the quasi-incompressible Navier–Stokes system
title_fullStr	An interpretation of Temam’s extra force in the quasi-incompressible Navier–Stokes system
title_full_unstemmed	An interpretation of Temam’s extra force in the quasi-incompressible Navier–Stokes system
title_sort	interpretation of temam’s extra force in the quasi-incompressible navier–stokes system
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/986d881b6e674a4aa48d9b2eddacac53
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An interpretation of Temam’s extra force in the quasi-incompressible Navier–Stokes system

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