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: $$\Vert \nabla \omega (t,\cdot ){\Vert }_{L^{\infty }}\gtrsim e^{At},\forall t\ge 0.$$

9 pages. arXiv admin note: text overlap with arXiv:1310.4799 by other authors

References in corpus (1)

• Infinite superlinear growth of the gradient for the two-dimensional Euler equation