9 citations · 16 across the 32 of their papers we have counts for
6 papers · 2 filters
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…