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

2016/08/25 by Zhen Lei, Jia Shi, Lei, Zhen +1
Engineering · Mathematics · #35Q31 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1608.07010

openalex publication_date 2016/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any A > 2, we construct solutions to the two-dimensional incompressible Euler equations on the torus \mathbbT² whose vorticity gradient ∇ω grows exponentially in time: ‖∇ω(t, ⋅)‖_L^∞ \gtrsim e^At, ∀ t ≥ 0.

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