Asymptotic analysis of the Stokes equations in a square at small viscosity

Abstract

Our aim in this article is to study the boundary layers appearing at small viscosity for the Stokes solutions in a square . By considering the Stokes problem in a square, we theoretically investigate the case where parabolic boundary layers are present. Using some divergence-free correctors, the asymptotic expansion of the viscous velocity solution is constructed and the uniform validity of the approximate solution is then proved.

Keywords:

• Boundary layer theory
• Stokes equations
• correctors
• singular perturbation

AMS Subject Classifications:

• 35C20
• 35B25
• 35K05

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by NSF [grant number DMS 1212141], [grant number DMS 1510249]; the Research Fund of Indiana University.