Fast growth of the vorticity gradient in symmetric smooth domains for 2D incompressible ideal flow

We construct an initial data for the two-dimensional Euler equation in a bounded smooth symmetric domain such that the gradient of vorticity in $L^{\mathrm{\infty }}$ grows as a double exponential in time for all time. Our construction is based on the recent result by Kiselev and \v{S}ver'{a}k.