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It is shown that if the angle of the corner $\\theta$ is strictly less than $\\pi/2$, the Lipschitz estimate of the vorticity at the corner is at most single exponential growth and the upper bound is sharp. %near the stagnation point. For the corner with the larger angle $\\pi/2 < \\theta <2\\pi$, $\\theta \\neq \\pi$, we construct an example of the vorticity which loses continuity instantaneously. For the case $\\theta \\le \\pi/2$, the vorticity remains continuous inside the domain. 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