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

作者：Liu, Cheng Jie^*; Wang, Ya Guang

来源：Applied Mathematics Letters, 2014, 34(1): 81-85.

DOI：10.1016/j.aml.2014.04.005

• Boundary layers
• Prandtl equations
• Two space variables
• 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 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.

• 出版日期2014-8
• 单位上海交通大学