Tobias Barker

Swirl ill-posedness for incompressible fluids in (sub)critical spaces

For the 3D Navier-Stokes equations with sufficiently smooth initial data having zero swirl $u_{0\theta}\equiv 0$, 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 initial data, w...