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Article Dans Une Revue Quarterly of Applied Mathematics Année : 2020

Unsteady 3D-Navier-Stokes System with Tresca's Friction Law

Imane Boussetouan
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Résumé

Motivated by extrusion problems, we consider a non-stationary incompress-ible 3D fluid flow with a non-constant (temperature dependent) viscosity, subjected to mixed boundary conditions with a given time dependent velocity on a part of the boundary and Tresca's friction law on the other part. We construct a sequence of approximate solutions by using a regularization of the free boundary condition due to friction combined with a particular penalty method, reminiscent of the " incompressibility limit " of compressible fluids, allowing to get better insights into the links between the fluid velocity and pressure fields. Then we pass to the limit with compactness arguments to obtain a solution to our original problem.
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Dates et versions

hal-01246704 , version 1 (19-12-2015)

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Mahdi Boukrouche, Imane Boussetouan, Laetitia Paoli. Unsteady 3D-Navier-Stokes System with Tresca's Friction Law. Quarterly of Applied Mathematics, 2020, 78, pp.525-543. ⟨10.1090/qam/1563⟩. ⟨hal-01246704⟩
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