9 citations · 16 across the 32 of their papers we have counts for
33 papers
Quantum Landau Damping with Coulomb Repulsion in the Whole Space
Dongfen Bian, Emmanuel Grenier, Laurent Laflèche +1
In this paper, we study the large time behavior of solutions to the linearized Hartree equation near a stable equilibrium which is homogeneous in space and investigate the quantum…
Couette-Taylor instabilities in the small gap regime: the very counter-rotating case
Dongfen Bian, Gérard Iooss
In this paper, we study the Couette-Taylor instability of a viscous fluid between two rotating cylinders in the small-gap, slow rescaled rotation rate, high Reynolds number regime,…
From linear to nonlinear instabilities with application to plasma columns
Dongfen Bian
This article addresses the problem of proving the nonlinear instability of an equilibrium starting from its linear instability when there is no existence theory for the correspondi…
Couette Taylor instabilities for counter-rotating cylinders in the small-gap regime
Dongfen Bian, Emmanuel Grenier, Gérard Iooss +1
We study the Couette Taylor instabilities for an incompressible viscous fluid between two coaxial cylinders of nearly equal radii, allowing counter-rotation with the ratio of rotat…
Subcritical bifurcations of shear flows
Dongfen Bian, Shouyi Dai, Emmanuel Grenier
It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier-Stokes equations if the viscosity is small enough, provided the hor…
Stability and instability of small BGK waves
Dongfen Bian, Emmanuel Grenier, Wenrui Huang +1
The aim of this article is to prove that the linear stability or instability of small Bernstein-Green-Kruskal (BGK) waves is determined by the sign of the derivative of their energ…
Couette Taylor instabilities in the small-gap regime
Dongfen Bian, Emmanuel Grenier, Gérard Iooss +1
The Couette-Taylor instability occurs in a viscous fluid confined between two coaxial rotating cylinders. When the Taylor number surpasses a critical value, the stable Couette flow…
The dispersion relation of Tollmien-Schlichting waves
Dongfen Bian, Shouyi Dai, Emmanuel Grenier
It is well-known that shear flows in a strip or in the half plane are unstable for the Navier-Stokes equations if the viscosity is small enough, provided the horizontal wave nu…
Bifurcations of viscous boundary layers in the half space
Dongfen Bian, Emmanuel Grenier, Gérard Iooss
It is well-established that shear flows are linearly unstable provided the viscosity is small enough, when the horizontal Fourier wave number lies in some interval, between the so-…
Landau damping in mixed hyperbolic-kinetic systems and thick sprays
D. Bian, B. Després, V. Fournet +1
This article is devoted to the study of a model of thick sprays which combines the Vlasov equation for the particles and the barotropic compressible Euler equations to describe the…
Bifurcations of viscous shear flows in a strip
Bian Dongfen, Grenier Emmanuel, Haragus Mariana
It is well-established that shear flows in a periodic strip are linearly unstable for the incompressible Navier Stokes equations provided the viscosity is small enough. In this art…
Boundary driven instabilities of Couette flows
Dongfen Bian, Emmanuel Grenier, Nader Masmoudi +1
In this article, we prove that the threshold of instability of the classical Couette flow in for large is . The instability is completely driven by the boundary.…
Singularities of Rayleigh equation
Dongfen Bian, Emmanuel Grenier
The Rayleigh equation, which is the linearized Euler equations near a shear flow in vorticity formulation, is a key ingredient in the study of the long time behavior of solutions o…
Boundary layer expansions of the steady MHD equations in a bounded domain
Dongfen Bian, Zhenjie Si
In this paper, we investigate the validity of boundary layer expansions for the MHD system in a rectangle. We describe the solution up to any order when the tangential magnetic fie…
Asymptotic behavior of solutions of the linearized Euler equations near a shear layer
Dongfen Bian, Emmanuel Grenier
In this article, thanks to a new and detailed study of the Green's function of Rayleigh equation near the extrema of the velocity of a shear layer, we obtain optimal bounds on the…
Linear stability analysis of the Couette flow for the 2D Euler-Poisson system
Xueke Pu, Wenli Zhou, Dongfen Bian
This paper is concerned with the linear stability analysis for the Couette flow of the Euler-Poisson system for both ionic fluid and electronic fluid in the domain $\bb{T}\times\bb…
Instability of shear layers and Prandtl's boundary layers
Dongfen Bian, Emmanuel Grenier
This paper is devoted to the study of the nonlinear instability of shear layers and of Prandtl's boundary layers, for the incompressible Navier Stokes equations. We prove that gene…
Instabilities of shear layers
Dongfen Bian, Emmanuel Grenier
This article gathers notes of two lectures given at Grenoble's University in June , and is an introduction to recent works on shear layers, in collaboration with D. Bian, Y.…
Asymptotic behaviour of solutions of linearized Navier Stokes equations in the long waves regime
Dongfen Bian, Emmanuel Grenier
The aim of this paper is to describe the long time behavior of solutions of linearized Navier Stokes equations near a concave shear layer profile in the long waves regime, namely f…
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 threshold for 2D shear flows near Couette of the Navier-Stokes equation
Dongfen Bian, Xueke Pu
In this paper, we consider the stability threshold of the 2D shear flow of the Navier-Stokes equation at high Reynolds number . When the shear flow is near in…
Stability of Couette flow for 2D Boussinesq system in a uniform magnetic field
Dongfen Bian, Shouyi Dai, Jingjing Mao
In this paper, we consider the Boussinesq equations with magnetohydrodynamics convection in the domain and establishes the nonlinear stability of the…
Stability threshold for 2D shear flows of the Boussinesq system near Couette
Dongfen Bian, Xueke Pu
In this paper, we consider the stability threshold for the shear flows of the Boussinesq system in a domain . The main goal is to prove the nonlinear…