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…
Green function for linearized Navier-Stokes around a boundary shear layer profile for long wavelengths
Emmanuel Grenier, Toan T. Nguyen
This paper is the continuation of a program, initiated in Grenier-Nguyen [8,9], to derive pointwise estimates on the Green function of Orr Sommerfeld equations. In this paper we fo…
Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method
Emmanuel Grenier, Toan T. Nguyen, Frédéric Rousset +1
We study the large time behavior of solutions to two-dimensional Euler and Navier-Stokes equations linearized about shear flows of the mixing layer type in the unbounded channel $\…
instability of Prandtl layers
Emmanuel Grenier, Toan T. Nguyen
In , Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of incompressible Navier Stokes equations near a boundary as the viscosity go…
On nonlinear instability of Prandtl's boundary layers: the case of Rayleigh's stable shear flows
Emmanuel Grenier, Toan T. Nguyen
In 1904, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of Navier Stokes equations near a boundary as the viscosity goes to . His An…
Green function for linearized Navier-Stokes around a boundary layer profile: near critical layers
Emmanuel Grenier, Toan T. Nguyen
This is a continuation and completion of the program (initiated in \cite{GrN1,GrN2}) to derive pointwise estimates on the Green function and sharp bounds on the semigroup of linear…
Sublayer of Prandtl boundary layers
Emmanuel Grenier, Toan T. Nguyen
The aim of this paper is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit: . In \cite{Grenier}, one of the authors proved that there…
Sharp bounds for the resolvent of linearized Navier Stokes equations in the half space around a shear profile
Emmanuel Grenier, Toan T. Nguyen
In this paper, we derive sharp bounds on the semigroup of the linearized incompressible Navier-Stokes equations near a stationary shear layer in the half plane and in the half spac…
Green function of Orr Sommerfeld equations away from critical layers
Emmanuel Grenier, Toan T. Nguyen
The classical Orr-Sommerfeld equations are the resolvent equations of the linearized Navier Stokes equations around a stationary shear layer profile in the half plane. In this pape…
Large scale asymptotics of velocity-jump processes and non-local Hamilton-Jacobi equations
Emeric Bouin, Vincent Calvez, Emmanuel Grenier +1
We investigate a simple velocity jump process in the regime of large deviation asymptotics. New velocities are taken randomly at a constant, large, rate from a Gaussian distributio…
Large time monotonicity of solutions of reaction-diffusion equations in R^N
Emmanuel Grenier, François Hamel
In this paper, we consider nonnegative solutions of spatially heterogeneous Fisher-KPP type reaction-diffusion equations in the whole space. Under some assumptions on the initial c…
Spectral stability of Prandtl boundary layers: an overview
Emmanuel Grenier, Yan Guo, Toan T. Nguyen
In this paper we show how the stability of Prandtl boundary layers is linked to the stability of shear flows in the incompressible Navier Stokes equations. We then recall classical…
Spectral instability of characteristic boundary layer flows
Emmanuel Grenier, Yan Guo, Toan T. Nguyen
In this paper, we construct growing modes of the linearized Navier-Stokes equations about generic stationary shear flows of the boundary layer type in a regime of sufficiently larg…
Spectral instability of symmetric shear flows in a two-dimensional channel
Emmanuel Grenier, Yan Guo, Toan Nguyen
This paper concerns spectral instability of shear flows in the incompressible Navier-Stokes equations with sufficiently large Reynolds number: . It is well-documented…