In d≥4, axisymmetric swirl-free Euler solutions allow potential finite-time blowup excluded in d=3, with a conditional blowup theorem whose condition weakens as d increases.
Sideris, and Pascal Gamblin, On the evolution of compactly supported planar vorticity , Comm
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On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions
In d≥4, axisymmetric swirl-free Euler solutions allow potential finite-time blowup excluded in d=3, with a conditional blowup theorem whose condition weakens as d increases.