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The scalar Oseen operator - Δ + / x 1 in 2

Chérif AmroucheHamid Bouzit — 2008

Applications of Mathematics

This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in L p theory.

Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations

Chérif AmrouchePatrick PenelNour Seloula — 2013

Annales mathématiques Blaise Pascal

This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.

Shape Sensitivity Analysis of the Dirichlet Laplacian in a Half-Space

Cherif AmroucheŠárka NečasováJan Sokołowski — 2004

Bulletin of the Polish Academy of Sciences. Mathematics

Material and shape derivatives for solutions to the Dirichlet Laplacian in a half-space are derived by an application of the speed method. The proposed method is general and can be used for shape sensitivity analysis in unbounded domains for the Neumann Laplacian as well as for the elasticity boundary value problems.

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