Lukas Niebel
Mathematician
Department of Mathematics
ETH Zürich
niebel.math@gmail.com
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Welcome!
I am a mathematician working in analysis and partial differential equations. My research interests include kinetic and hypoelliptic equations, nonlinear diffusion, and free-boundary problems in fluid mechanics. More broadly, I am interested in the interplay between transport, geometry, and regularity in nonlinear PDEs.
News
- August 2026 — I started a new position at ETH Zurich in Mikaela Iacobelli's group. I'm really happy to be here!
- July 2026 — Lisa, ChatGPT and I prove kinetic trace estimates and construct related counterexamples, thereby resolving the previously open kinetic trace problem. [Preprint]
- May 2026 — In a new preprint I prove kinetic Gagliardo-Nirenberg inequalities for nonlocal diffusions. These inequalites are adapted to the study of the kinetic \(p\)-Laplace equation with nonlocal diffusion. [Preprint]
- May 2026 — Together with Helge and Rico we prove kinetic Gagliardo-Nirenberg inequalities in a new preprint. This opens up the study of the kinetic \(p\)-Laplace equation, where we prove local boundedness of weak subsolutions. [Preprint]
- May 2026 — I uploaded a revised version of my work on global rigidity of two dimensional bubbles where I do now prove the theorems in their sharp range \( 0 \le \mathrm{We} \le 3 \). [Preprint]
- May 2026 — I explain how to use kinetic trajectories to prove transfer of regularity à la Bouchut-Hörmander in a short note. [Preprint]
Meet me here
- August 2026 — I'm going to give a talk during the "Workshop on Nonlinear PDEs, Harmonic Analysis and FBPs" in Stockholm. [Event]
- January 2027 — I'll be in Vienna for the workshop "Dynamics across Scales: Bridging Kinetic Theory and Fluid Mechanics". [Event]
- July 2027 — Time to fly to Singapore for the workshop "Nonlocal Interaction Models". [Event]
Short Bio
- 2026 — present Postdoctoral researcher at ETH Zürich in the group of Mikaela Iacobelli.
- 2023 — 2026 Postdoctoral researcher at the University of Münster in the group of Christian Seis.
- 2019 — 2023 PhD student at Ulm University under the supervision of Rico Zacher.
- 2014 — 2019 BSc and Msc in Mathematics at Ulm University, Germany.