  In this paper, the two dimensional Euler flow under a simple symmetry
condition with hyperbolic structure in a unit square
$D=\{(x_1,x_2):0<x_1+x_2<\sqrt{2},0<-x_1+x_2<\sqrt{2}\}$ is considered. It is
shown that the Lipschitz estimate of the vorticity on the boundary is at most
single exponential growth near the stagnation point.
