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

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 zer...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2016; no. 235; pp. 1 - 13
Main Authors Hani Ali, Petr Kaplicky
Format Journal Article
LanguageEnglish
Published Texas State University 26.08.2016
Subjects
existence of solutions
Turbulence model
weak solution
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ISSN1072-6691

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Summary: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.
ISSN:1072-6691