Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations

Amrouche, Chérif; Penel, Patrick; Seloula, Nour El Houda

doi:10.5802/ambp.321

Cited by 15 publications

(2 citation statements)

References 22 publications

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“…Theorem 1.1. Let Ω be the domain given in (5). For any flux Φ, the Navier-Stokes system (1), (2), and (4) has a solution u = g + v, where g is a smooth vector field satisfying (6)…”

Section: Introductionmentioning

confidence: 99%

On the Leray problem for steady flows in two-dimensional infinitely long channels with slip boundary conditions

Sha¹,

Wang²,

Xie³

2022

Preprint

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In this paper, we investigate the Leray problem for steady Navier-Stokes system under full slip boundary conditions in a two dimensional channel with straight outlets. The existence of solutions with arbitrary flux in a general channel with slip boundary conditions is established, which tend to uniform flows at far fields. Furthermore, if the flux is suitably small, the solutions are proved to be unique. One of the crucial ingredients is to construct an appropriate flux carrier and to show a Hardy type inequality for flows with full slip boundary conditions.

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“…Theorem 1.1. Let Ω be the domain given in (5). For any flux Φ, the Navier-Stokes system (1), (2), and (4) has a solution u = g + v, where g is a smooth vector field satisfying (6)…”

Section: Introductionmentioning

confidence: 99%

On the Leray problem for steady flows in two-dimensional infinitely long channels with slip boundary conditions

Sha¹,

Wang²,

Xie³

2022

Preprint

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show abstract

“…Many works took inspiration from Serrin's observation. Here we mention [10], where the authors addressed theoretical questions related to the choice of boundary conditions. In the last decade, free-slip boundary conditions for the Rayleigh-Bénard convection problem have been considered and rigorous upper bounds on the Nusselt number indicate the possibility of enhanced heat transport compared to the no-slip case.…”

Section: Introductionmentioning

confidence: 99%

The role of boundary conditions in scaling laws for turbulent heat transport

Nobili¹

2021

Preprint

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In most results concerning bounds on the heat transport in the Rayleigh-Bénard convection problem no-slip boundary conditions for the velocity field are assumed. Nevertheless it is debatable, whether these boundary conditions reflect the behavior of the fluid at the boundary. This problem is important in theoretical fluid mechanics as well as in industrial applications, as the choice of boundary conditions has effects in the description of the boundary layers and its properties. In fact, different boundary conditions may inhibit or enhance heat transport. This review presents a selection of contributions in the theory of rigorous bounds on Nusselt number, distinguishing and comparing the results for no-slip, free-slip and Navier-slip boundary conditions.

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Evolutionary NS-TKE Model

Rebollo

Lewandowski

2014

Mathematical and Numerical Foundations of Turbulence Models and Applications

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Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations

Cited by 15 publications

References 22 publications

On the Leray problem for steady flows in two-dimensional infinitely long channels with slip boundary conditions

On the Leray problem for steady flows in two-dimensional infinitely long channels with slip boundary conditions

The role of boundary conditions in scaling laws for turbulent heat transport

Evolutionary NS-TKE Model

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