Makram Hamouda

Asymptotic analysis of the Stokes problem on general bounded domains: the case of a characteristic boundary

The goal of this article is to study the asymptotic behaviour of the solutions of linearized Navier–Stokes equations (LNSE), when the viscosity is small, in a general (curved) bounded and smooth domain in ℝ3 with a characteristic boundary. To handle the difficulties due to the curvature of the boundary, we first introduce a curvilinear coordinate system which is adapted to the boundary. Then we prove the existence of a strong corrector for the LNSE. More precisely, we show that the solution of LNSE behaves like the corresponding Euler solution except in a thin region, near the boundary, where a certain heat solution is added as a corrector.

Asymptotic analysis of the Navier-Stokes equations in a curved domain with a non-characteristic boundary

We consider the Navier-Stokes equations of an incompressible fluid in a three dimensional curved domain with permeable walls in the limit of small viscosity. Using a curvilinear coordinate system, adapted to the boundary, we construct a corrector function at order

New Finite Volume Method for rotating channel flows involving boundary layers

e^j

SOME SINGULAR PERTURBATION PROBLEMS RELATED TO THE NAVIER-STOKES EQUATIONS

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Boundary layers in smooth curvilinear domains: Parabolic problems

j=0,1

BOUNDARY LAYERS FOR THE NAVIER-STOKES EQUATIONS. THE CASE OF A CHARACTERISTIC BOUNDARY

, where

Boundary layers for the 2D linearized primitive equations

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Boundary layers for the 3D primitive equations in a cube: The supercritical modes

is the (small) viscosity parameter. This allows us to obtain an asymptotic expansion of the Navier-Stokes solution at order

Asymptotic analysis for the 3D primitive equations in a channel

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Existence and Regularity Results for the Inviscid Primitive Equations with Lateral Periodicity

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