Derivation of Prandtl boundary layer equations for the incompressible Navier–Stokes equations in a curved domain

The proposal of this note is to derive the equations of boundary layers in the small viscosity limit for the two-dimensional incompressible Navier–Stokes equations defined in a curved bounded domain with the non-slip boundary condition. By using curvilinear coordinate system in a neighborhood of bou...

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Bibliographic Details
Published in:Applied mathematics letters 2014-08, Vol.34, p.81-85
Main Authors: Liu, Cheng-Jie, Wang, Ya-Guang
Format: Article
Language:English
Subjects:
Boundaries
Boundary layer
Boundary layers
Curved
Curved domain
Derivation
Incompressible flow
Mathematical analysis
Navier-Stokes equations
Prandtl equations
Two space variables
Viscosity
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Summary:The proposal of this note is to derive the equations of boundary layers in the small viscosity limit for the two-dimensional incompressible Navier–Stokes equations defined in a curved bounded domain with the non-slip boundary condition. By using curvilinear coordinate system in a neighborhood of boundary, and the multi-scale analysis we deduce that the leading profiles of boundary layers of the incompressible flows in a bounded domain still satisfy the classical Prandtl equations when the viscosity goes to zero, which are the same as for the flows defined in the half space.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2014.04.005