On the blowup rate of vorticity for the Euler equations in a bounded domain
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913056690274304 |
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| author | Ingimarson, Benjamin Kukavica, Igor |
| author_facet | Ingimarson, Benjamin Kukavica, Igor |
| contents | 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 $\|D^kω\|_{L^\infty(Ω)}$ for $k \geq 1$. We also show that the Gronwall-type inequality satisfied by $\|ω(t)\|_{L^\infty}$, in the cases that $Ω= \mathbb{R}^3$, $\mathbb{T}^3$, or a bounded domain, exhibits wildly oscillating solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21299 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the blowup rate of vorticity for the Euler equations in a bounded domain Ingimarson, Benjamin Kukavica, Igor Analysis of PDEs 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 $\|D^kω\|_{L^\infty(Ω)}$ for $k \geq 1$. We also show that the Gronwall-type inequality satisfied by $\|ω(t)\|_{L^\infty}$, in the cases that $Ω= \mathbb{R}^3$, $\mathbb{T}^3$, or a bounded domain, exhibits wildly oscillating solutions. |
| title | On the blowup rate of vorticity for the Euler equations in a bounded domain |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.21299 |