Analysis of the Leray-α model with Navier slip boundary condition

2011/07/28 by Hani Ali, Ali, Hani, Petr Kaplický +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math-ph #math.AP #math.MP #msc:35Q30 #msc:35Q35 #msc:76B03 #msc:76F65

paper · pdf · doi:10.48550/arxiv.1107.5718

13 pages

arxiv created 2011/07/28 · arxiv updated 2011/07/29

Abstract

In this paper, we establish the existence and the regularity of a unique weak solution to turbulent flows in a bounded domain Ω⊂ \mathbb R³ governed by the so-called Leray-α model. We consider the Navier slip boundary conditions for the velocity. Furthermore, we show that, when the filter coefficient α tends to zero, the weak solution constructed converges to a suitable weak solution to the incompressible Navier Stokes equations subject to the Navier boundary condition. Similarly, if λ tends to 1- we recover a solution to the Leray-α model with the homogeneous Dirichlet boundary conditions.

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