Infinite-time Exponential Growth of the Euler Equation on Two-dimensional Torus

Abstract: For any $A > 2$, we construct solutions to the two-dimensional incompressible Euler equations on the torus $\mathbb{T}^2$ whose vorticity gradient $\nabla\omega$ grows exponentially in time: $$|\nabla\omega(t, \cdot)|_{L^\infty} \gtrsim e^{At},\quad \forall\ t \geq 0.$$