Lukas Niebel
Postdoctoral researcher
Analysis & PDE
Applied Mathematics Münster
University of Münster
niebel.math@gmail.com
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Welcome!
I am postdoctoral researcher at the University Münster. I am a member of the research group of Christian Seis
where we will be studying surface tension effects in ideal fluids. Moreover, I work on the regularity theory of kinetic partial differential equations, including the \( L^p \) theory of weak and strong solutions and the De Giorgi–Nash–Moser theory,
with the goal of unraveling the secrets of the underlying kinetic geometry.
News
- August 2025 — New Preprint on the arXiv. Together with Clément, Helge and Rico we study critical kinetic trajectories. As applications we transfer the Moser-Bombieri-Giusti approach to the kinetic setting to obtain optimal Harnack inequalities and give an elementary proof of the kinetic Sobolev inequality. [Preprint]
- July 2025 — The article on trajectories and Moser's proof of the Harnack inequality, co-authored with Rico, has been published in the Annali Scuola Normale Superiore Di Pisa. [Article]
- May 2025 — I presented the work together with Christian and David on bubbles and drops in inviscid fluids at the Nonlinear PDE Seminar in Karlsruhe. Thank you Björn and Jannis for hosting me. [Slides] [Event]
- April 2025 — The article, where together with Cyril and Pascal we construct the fundamental solution for the Kolmogorov equation with rough coefficients, has been published in SIAM Journal on Mathematical Analysis. [Article] [arXiv]
- February 2025 — Together with Christian and David we uploaded our work on steady vortex bubbles and drops in inviscid fluids to the arXiv. [Preprint]
- February 2025 — The article on kinetic trajectories, co-authored with Rico, has been published in the Journal of Functional Analysis. [Article]
- February 2025 — I am very grateful to have recieved the PhD thesis award “Promotionspreis der Ulmer Universitätsgesellschaft”. [Event]