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

作者：Gie Gung Min^*; Hamouda Makram; Temam Roger

来源：Applicable Analysis, 2010, 89(1): 49-66.

DOI：10.1080/00036810903437796

• boundary layers
• singular perturbations
• Stokes equations
• curvilinear coordinates

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 3 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.

• 出版日期2010