Boundary layer separation and local behavior for the Steady Prandtl equation

Abstract

In the case of favorable pressure gradient, Oleinik proved the global existence of classical solution for the 2-D steady Prandtl equation for a class of positive data. In the case of adverse pressure gradient, an important physical phenomena is the boundary layer separation. In this paper, we prove the boundary layer separation for a large class of Oleinik's data and confirm Goldstein's hypothesis concerning the local behavior of the solution near the separation, which gives a partial answer to open problem 5 proposed by Oleinik and Samokin in \cite{Olei}.

17 pages

References in corpus (1)

• Separation of the two-dimensional unsteady Prandtl boundary layers under an adverse pressure gradient

Cited by in corpus (5)

• Global-in-$x$ Stability of Steady Prandtl Expansions for 2D Navier-Stokes Flows
• Boundary Layer Expansions for the Stationary Navier-Stokes Equations
• On the global small solution of 2-D Prandtl system with initial data in the optimal Gevrey class
• Global $C^{\infty }$ Regularity of the Steady Prandtl Equation
• Separation of the two-dimensional unsteady Prandtl boundary layers under an adverse pressure gradient