Electron. J. Differential Equations, Vol. 2016 (2016), No. 235, pp. 1-13.

Existence and regularity of solutions to the Leray-alpha model with Navier slip boundary conditions

Hani Ali, Petr Kaplicky

We establish the existence and regularity of a unique weak solution to turbulent flows in a bounded domain $\Omega\subset\mathbb R^3$ governed by the Leray-alpha model with Navier slip boundary condition for the velocity. Furthermore, we show that when the filter coefficient alpha tends to zero, these weak solutions converge to a suitable weak solution to the incompressible Navier Stokes equations subject to the Navier boundary conditions. Finally, we discuss the relation between the Leray-alpha model and the Navier-Stokes equations with homogeneous Dirichlet boundary condition.

Submitted April 15, 2013. Published August 26, 2016.
Math Subject Classifications: 35Q30, 35Q35, 76F60.
Key Words: Turbulence model; existence of solutions; weak solution.

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Hani Ali
AXA Global P & C
Paris, France
email: hani.ali@axa.com
Petr Kaplicky
Charles University
Faculty of Mathematics and Physics
Sokolovska 83
186 75 Prague 8, Czech Republic
email: kaplicky@karlin.mff.cuni.cz

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