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arXiv · 2204.13406

On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions

Evan Miller·Tai-Peng Tsai
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Abstract

In this paper, we consider axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions. We show that in dimension $d\geq 4$, axisymmetric, swirl-free solutions of the Euler equation have properties which could allow finite-time singularity formation of a form that is excluded when $d=3$, and we prove a conditional blowup result for axisymmetric, swirl-free solutions of the Euler equation in dimension $d\geq 4$. The condition which must be imposed on the solution in order to imply blowup becomes weaker as $d\to +\infty$, suggesting the dynamics are becoming much more singular as the dimension increases.

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Evan Miller, Tai-Peng Tsai. 2022-04-28. On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions. https://doi.org/10.4171/rmi%2F1616

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