Boundary Layers of Time-Dependent Convection-Diffusion Equations in a Square

The aim of this paper is to study the asymptotic behavior for a class of time-dependent convection-diffusion problems in a square = ( 0,1 ) x ( 0, 1), which is a simplified model of the Oseen equations. By considering this problem in a square, we theoretically treat the case where parabolic and ordinary boundary layers are present. We construct correctors which absorb the singularities of the limit solution; this allows to obtain an approximation of the viscous solution up to the boundary. The expression of the correctors is giving explicitly and the uniform validity of the approximate solution is then proved.