61 citations · 216 across the 24 of their papers we have counts for
21 papers · 1 filter
H{ö}lder regularity of parabolic equations with Dirichlet boundary conditions and application to reaction-diffusion and reaction-cross-diffusion systems
Hector Bouton, Laurent Desvillettes, Helge Dietert
In this work, we adapt our recent article [BDD25] to the setting of Dirichlet boundary conditions. A key part is the study of the parabolic equation with a…
Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions
Hector Bouton, Laurent Desvillettes, Helge Dietert
We prove the existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lokta-Volterra reaction terms in three dimensions.…
Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions
Hector Bouton, Laurent Desvillettes, Helge Dietert
We prove the existence of global strong solutions to the triangular Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system with Lokta-Volterra reaction terms in three dimensions.…
Study of a class of triangular starvation driven cross-diffusion systems
Elisabetta Brocchieri, Laurent Desvillettes, Helge Dietert
We study the existence, regularity and uniqueness for a general class of triangular reaction-cross-diffusion systems coming from the study of starvation driven behavior for two spe…
Nonlinear stability for active suspensions
Michele Coti Zelati, Helge Dietert, David Gérard-Varet
This paper is devoted to the nonlinear analysis of a kinetic model introduced by Saintillan and Shelley to describe suspensions of active rodlike particles in viscous flows. We inv…
Regularity for rough hypoelliptic equations
Helge Dietert, Jonas Hirsch
We present a general approach to obtain a weak Harnack inequality for rough hypoellipitic equations, e.g. kinetic equations. The proof is constructive and does not study the commut…
Stability and cascades for the Kolmogorov-Zakharov spectrum of wave turbulence
Charles Collot, Helge Dietert, Pierre Germain
The kinetic wave equation arises in wave turbulence to describe the Fourier spectrum of solutions to the cubic Schroedinger equation. The equation has two Kolmogorov-Zakharov stead…
Quantitative Geometric Control in Linear Kinetic Theory
Helge Dietert, Frédéric Hérau, Harsha Hutridurga +1
We consider general linear kinetic equations combining transport and a linear collision on the kinetic variable with a spatial weight that can vanish on part of the domain. The con…
Orientation mixing in active suspensions
Michele Coti Zelati, Helge Dietert, David Gérard-Varet
We study a popular kinetic model introduced by Saintillan and Shelley for the dynamics of suspensions of active elongated particles where the particles are described by a distribut…
On the ill-posedness of the triple deck model
Helge Dietert, David Gérard-Varet
We analyze the stability properties of the so-called triple deck model, a classical refinement of the Prandtl equation to describe boundary layer separation. Combining the methodol…
Finding the jump rate for fastest decay in the Goldstein-Taylor model
Helge Dietert, Josephine Evans
For hypocoercive linear kinetic equations we first formulate an optimisation problem on a spatially dependent jump rate in order to find the fastest decay rate of perturbations. In…
Persisting entropy structure for nonlocal cross-diffusion systems
Helge Dietert, Ayman Moussa
For cross-diffusion systems possessing an entropy (i.e. a Lyapunov functional)we study nonlocal versions and exhibit sufficient conditions to ensure that thenonlocal version inheri…
Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit
Elisabetta Brocchieri, Lucilla Corrias, Helge Dietert +1
We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two…
On Cucker-Smale dynamical systems with degenerate communication
Helge Dietert, Roman Shvydkoy
This note introduces a new method for establishing alignment in systems of collective behavior with degenerate communication protocol. The communication protocol consists of a kern…
Well-posedness of the Prandtl equation without any structural assumption
Helge Dietert, David Gerard-Varet
We show the local in time well-posedness of the Prandtl equation for data with Gevrey regularity in and regularity in . The main novelty of our result is that we d…
About the entropic structure of detailed balanced multi-species cross-diffusion equations
Esther S. Daus, Laurent Desvillettes, Helge Dietert
This paper links at the formal level the entropy structure of a multi-species cross-diffusion system of Shigesada-Kawasaki-Teramoto (SKT) type satisfying the detailed balance condi…
The mathematics of asymptotic stability in the Kuramoto model
Helge Dietert, Bastien Fernandez
Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phen…
High frequency analysis of the unsteady Interactive Boundary Layer model
Anne-Laure Dalibard, Helge Dietert, David Gérard-Varet +1
The present paper is about a famous extension of the Prandtl equation, the so-called Interactive Boundary Layer model (IBL). This model has been used intensively in the numerics of…
Stability of partially locked states in the Kuramoto model through Landau damping with Sobolev regularity
Helge Dietert
The Kuramoto model is a mean-field model for the synchronisation behaviour of oscillators, which exhibits Landau damping. In a recent work, the nonlinear stability of a class of sp…
Landau damping to partially locked states in the Kuramoto model
Helge Dietert, Bastien Fernandez, David Gérard-Varet
In the Kuramoto model of globally coupled oscillators, partially locked states (PLS) are stationary solutions that incorporate the emergence of partial synchrony when the interacti…
Stability and bifurcation for the Kuramoto model
Helge Dietert
We study the mean-field limit of the Kuramoto model of globally coupled oscillators. By studying the evolution in Fourier space and understanding the domain of dependence, we show…