Unsteady 3D-Navier-Stokes System with Tresca's Friction Law
Analysis of PDEs
2015-12-22 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1512.06607,
title = {Unsteady 3D-Navier-Stokes System with Tresca's Friction Law},
author = {Mahdi Boukrouche and Imane Boussetouan and Laetitia Paoli},
journal= {arXiv preprint arXiv:1512.06607},
year = {2015}
}