Author

Lukas Niebel

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Preprint Aug 2026

Lions'Maximal Regularity Problem for Divergence-Form Differential Operators: Failure at the $\frac{1}{2}$-H\"older Endpoint

In this work we give a counterexample to maximal $\mathrm{L}^2$-regularity in Lions'problem for divergence-form differential operators. On a bounded interval, we construct a bounded, uniformly elliptic, real scalar diffusion coefficient that is $\frac{1}{2}$-H\"older continuous in time with values in spatial $\mathrm{L...

Lukas Niebel · 0 citations

Preprint Aug 2026

On Leonardo da Vinci's paradox

Buoyancy points straight upward, yet in the absence of external forces, a rising air bubble may trace a spiral through the water. This phenomenon was already observed by Leonardo da Vinci. We show that the gravity-free, three-dimensional two-phase incompressible Euler equations with surface tension already admit such a...

Björn Gebhard, Lukas Niebel, Christian Seis · 0 citations

Preprint Aug 2026

A Liouville theorem for the two-dimensional stationary hypodissipative Navier--Stokes system

We study the two-dimensional stationary incompressible Navier--Stokes equations on $\mathbb R^2$ with fractional dissipation $(-\Delta)^s$. In the full range $s \in (0,1)$, we prove that every smooth solution satisfying the natural energy condition $u\in\dot{\mathrm H}^s(\mathbb R^2;\mathbb R^2)$ has $u\equiv0$ and con...

Nicola De Nitti, Lukas Niebel, Jia-Qi Yang · 0 citations