10 citations · 16 across the 20 of their papers we have counts for
21 papers
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…
Nash's bound for the Kolmogorov equation
Helge Dietert, Lukas Niebel
We prove Nash's bound for the Kolmogorov equation with rough coefficients. Our proof is inspired by the treatment of the parabolic problem by Nash (1958) and Fabes and Stroock…
Global rigidity of two-dimensional bubbles
Lukas Niebel
We study bubbles, which are stationary hollow vortices with surface tension, in two dimensions. Such objects solve an overdetermined elliptic free boundary problem in an exterior d…
Critical trajectories in kinetic geometry
Helge Dietert, Clément Mouhot, Lukas Niebel +1
We construct critical trajectories in kinetic geometry, i.e. curves in that are: tangential to the vector fields and , co…
Steady bubbles and drops in inviscid fluids
David Meyer, Lukas Niebel, Christian Seis
We construct steady non-spherical bubbles and drops, which are traveling wave solutions to the axisymmetric two-phase Euler equations with surface tension, whose inner phase is a b…
Fundamental solutions to Kolmogorov-Fokker-Planck equations with rough coefficients: existence, uniqueness, upper estimates
Pascal Auscher, Cyril Imbert, Lukas Niebel
We show the existence and uniqueness of fundamental solution operators to Kolmo\-gorov-Fokker-Planck equations with rough (measurable) coefficients and local or integral diffusion…
Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness
Pascal Auscher, Cyril Imbert, Lukas Niebel
We prove existence, uniqueness and regularity of weak solutions of Kolmogorov--Fokker--Planck equations with either local or non-local diffusion in the velocity variable and rough…
A trajectorial interpretation of Moser's proof of the Harnack inequality
Lukas Niebel, Rico Zacher
In 1971 Moser published a simplified version of his proof of the parabolic Harnack inequality. The core new ingredient is a fundamental lemma due to Bombieri and Giusti, which comb…
On a kinetic Poincaré inequality and beyond
Lukas Niebel, Rico Zacher
In this article, we give a trajectorial proof of a kinetic Poincaré inequality which plays an important role in the De Giorgi-Nash-Moser theory for kinetic equations. The present w…
Kinetic maximal -regularity for the fractional Kolmogorov equation with variable density
Lukas Niebel
We consider the Kolmogorov equation, where the right-hand side is given by a non-local integro-differential operator comparable to the fractional Laplacian in velocity with possibl…
Kinetic maximal -regularity with temporal weights and application to quasilinear kinetic diffusion equations
Lukas Niebel, Rico Zacher
We introduce the concept of kinetic maximal -regularity with temporal weights and prove that this property is satisfied for the (fractional) Kolmogorov equation. We show that…
Kinetic maximal -regularity for the (fractional) Kolmogorov equation
Lukas Niebel, Rico Zacher
We introduce the notion of kinetic maximal -regularity with temporal weights for the (fractional) Kolmogorov equation. In particular, we determine the function spaces for the…