6 papers · 1 filter
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…
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…
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…
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…