摘要：

In this paper, we study the occurrence of a back-flow point of the two-dimensional unsteady Prandtl boundary layer under an adverse pressure gradient. For the two-dimensional unsteady Prandtl boundary layer equations, when the initial tangential velocity is strictly monotonic with respect to the normal variable, and the pressure gradient of the outer flow is adverse, we obtain that the first critical point of the tangential velocity profile with respect to the normal variable, if it exists when the boundary layer evolves in time, must appear on the boundary. Moreover, we give a condition on the growth rate of the initial tangential velocity such that there is a back-flow point of the Prandtl boundary layer under the adverse pressure gradient. In the appendix, we present two examples showing that the back-flow point appears either when the flow distance is long in the streamwise direction for a given initial monotonic tangential velocity field or when the initial tangential velocity grows slowly in a large neighborhood of the boundary for a fixed flow distance in the streamwise direction.

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