10 citations · 16 across the 20 of their papers we have counts for
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Lions' Maximal Regularity Problem for Divergence-Form Differential Operators: Failure at the -Hölder Endpoint
Lukas Niebel
In this work we give a counterexample to maximal -regularity in Lions' problem for divergence-form differential operators. On a bounded interval, we construct a bound…
A Liouville theorem for the two-dimensional stationary hypodissipative Navier--Stokes system
Nicola De Nitti, Lukas Niebel, Jiaqi Yang
We study the two-dimensional stationary incompressible Navier--Stokes equations on with fractional dissipation . In the full range , we prove tha…
On Leonardo da Vinci's paradox
Björn Gebhard, Lukas Niebel, Christian Seis
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 d…
A fast dynamo with zero topological entropy
Lukas Niebel
We construct an autonomous Lipschitz fast dynamo on the flat three-torus whose particle flow has zero topological entropy and whose ideal induction equation has no exponential grow…
Sharp kinetic trace theory
Lukas Niebel, Lisa Valentini
We establish sharp kinetic trace estimates and counterexamples across several velocity models. For half-space position domains, without any common bound on velocity support, we pro…
Transfer of regularity by kinetic mollification along critical trajectories
Lukas Niebel
We give a trajectory-based proof of transfer-of-regularity estimates à la Bouchut-Hörmander for kinetic equations at the weak scale of local diffusion. The proof is based on kineti…
On the kinetic -Laplace equation with nonlocal diffusion
Lukas Niebel
We study two nonlocal versions of the kinetic -Laplace equation: a Gagliardo-type model defined through differences and a Bessel-type model defined via Fourier multiplication. U…
Nonlinear Kinetic Diffusion Equations with -Growth
Helge Dietert, Lukas Niebel, Rico Zacher
We establish the local boundedness of (sub-)solutions to nonlinear kinetic diffusion equations with -growth, where the kinetic p-Laplace equation is a prototypical example. A ke…
Spherical rigidity for an exterior overdetermined problem with Neumann data prescribed by mean curvature
Lukas Niebel
We study an overdetermined elliptic free boundary problem for exterior domains in , , introduced by F. Morabito [Comm. PDE 46 (2021), 1137-1161]. The overdet…
Kinetic Sobolev Spaces
Pascal Auscher, Lukas Niebel
We define and study homogeneous kinetic Sobolev spaces adapted to the Kolmogorov equation. We consider both local and non-local diffusion. The spaces are built from the Lebesgue sp…