Author

Ruilin Hu

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Preprint Oct 2026

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...

Tobias Barker, Rui-Lin Hu · 0 citations

Preprint Aug 2026

Well-posedness for the mean curvature flow on the half-space and on bounded domains

We study graphical mean curvature flow in arbitrary codimension over the half-space and over smooth bounded domains, subject to homogeneous Dirichlet boundary conditions. At the scaling-critical Lipschitz regularity, we prove local well-posedness for initial graphs that can be approximated in $W^{1,\infty}$ by smooth p...

Ke Chen, Ruilin Hu, Quoc-Hung Nguyen · 0 citations