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arXiv · 2604.21299

On the blowup rate of vorticity for the Euler equations in a bounded domain

Benjamin Ingimarson·Igor Kukavica
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Abstract

Given that a solution to the 3D incompressible Euler equations on a bounded domain blows up at a time $T_\ast$ and that $T_\ast$ is the first such time, we provide pointwise-in-time lower bounds on $\|D^k\omega\|_{L^\infty(\Omega)}$ for $k \geq 1$. We also show that the Gronwall-type inequality satisfied by $\|\omega(t)\|_{L^\infty}$, in the cases that $\Omega = \mathbb{R}^3$, $\mathbb{T}^3$, or a bounded domain, exhibits wildly oscillating solutions.

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Benjamin Ingimarson, Igor Kukavica. 2026-04-23. On the blowup rate of vorticity for the Euler equations in a bounded domain. https://arxiv.org/abs/2604.21299

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