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Swirl ill-posedness for incompressible fluids in (sub)critical spaces
For the 3D Navier-Stokes equations with sufficiently smooth initial data having zero swirl $u_{0θ}\equiv 0$, Ladyzhenskaya \cite{L1968} and Ukhovskii and Yudovich \cite{UY1968} established global regularity. It has since remained open as to whether well-posedness still holds for smooth axisymmetric
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