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Infinite-time Exponential Growth of the Euler Equation on Two-dimensional Torus (1608.07010v1)
Published 25 Aug 2016 in math.AP
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: $$|\nabla\omega(t, \cdot)|_{L\infty} \gtrsim e{At},\quad \forall\ t \geq 0.$$
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