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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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Elsevier
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/986d881b6e674a4aa48d9b2eddacac53 |
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| Sumario: | 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. |
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