91 citations · 143 across the 14 of their papers we have counts for
19 papers · 1 filter
Onset of nonlinear instabilities in monotonic viscous boundary layers
Dongfen Bian, Emmanuel Grenier
In this paper we study the nonlinear stability of a shear layer profile for Navier Stokes equations near a boundary. This question plays a major role in the study of the inviscid l…
Long waves instabilities
Dongfen Bian, Emmanuel Grenier
The aim of this paper is to give a detailed presentation of long wave instabilities of shear layers for Navier Stokes equations, and in particular to give a simple and easy to read…
Stability of shear flows near a boundary
Emmanuel Grenier, Toan T. Nguyen
This book is devoted to the study of the linear and nonlinear stability of shear flows and boundary layers for Navier Stokes equations for incompressible fluids with Dirichlet boun…
Plasma echoes near stable Penrose data
Emmanuel Grenier, Toan T. Nguyen, Igor Rodnianski
In this paper we construct particular solutions to the classical Vlasov-Poisson system near stable Penrose initial data on that are a combination of…
Landau damping for analytic and Gevrey data
Emmanuel Grenier, Toan T. Nguyen, Igor Rodnianski
In this paper, we give an elementary proof of the nonlinear Landau damping for the Vlasov-Poisson system near Penrose stable equilibria on the torus $\mathbb{T}^d \times \mathbb{R}…
Generator functions and their applications
Emmanuel Grenier, Toan T. Nguyen
In [Grenier-Nguyen], we introduced so called {\em generators} functions to precisely follow the regularity of analytic solutions of Navier Stokes equations. In this short note, we…