Remark on single exponential bound of the vorticity gradient for the two-dimensional Euler flow around a corner

Abstract

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.