| We consider the solutions of the non-stationary two dimensional Prandtl's system. This boundary layer equation is suggested by Prandtl in 1904. We have proved a global existence of solutions of this problem in the class that the vorticity has a distinguished sign, which was once studied by Oleinik provided that $p_x \leq 0$. This result solves an open problem proposed by Oleinik in their recent book. This is a jointed work with Z. P. Xin. |