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Error estimates for Stokes problem with Tresca friction conditions

Mekki Ayadi, Leonardo Baffico, Mohamed Khaled Gdoura, Taoufik Sassi (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we present and study a mixed variational method in order to approximate, with the finite element method, a Stokes problem with Tresca friction boundary conditions. These non-linear boundary conditions arise in the modeling of mold filling process by polymer melt, which can slip on a solid wall. The mixed formulation is based on a dualization of the non-differentiable term which define the slip conditions. Existence and uniqueness of both continuous and discrete solutions of these...

Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in n

Reinhard Farwig, Hermann Sohr (2009)

Czechoslovak Mathematical Journal

For a bounded domain Ω n , n 3 , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system - Δ u + u · u + p = f , div u = k , u | Ω = g with u L q , q n , and very general data classes for f , k , g such that u may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of...

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