Boundary layers for the Navier - Stokes equations : asymptotic analysis

In this article, we simplify and improve the asymptotic analysis of the solutions of the NavierStokes problem given in [8]. This problem is characterized by the presence of a small term which corresponds to the inverse of Reynolds number Re very large for the Navier-Stokes equations (Re >> 1). This small parameter is called the viscosity and denoted hereafter ε (ε = 1/Re). Thus, when the viscosity ε goes to zero, a particular phenomenon named boundary layers occurs in the interior or near the boundary of the domain considered for the Navier-Sotkes problem. The comprehension of these boundary layers makes the subject of many scientific works. For the mathematical point of view, see for example [4], [5], [6], [7], and [9] among many others.