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pro vyhledávání: '"Bian, Dongfen"'
In this article, we prove that the threshold of instability of the classical Couette flow in $H^s$ for large $s$ is $\nu^{1/2}$. The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of wi
Externí odkaz:
http://arxiv.org/abs/2409.00307
Autor:
Bian, Dongfen, Grenier, Emmanuel
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 of linearized Euler equations, in the study of the linear stability of
Externí odkaz:
http://arxiv.org/abs/2408.00977
Autor:
Bian, Dongfen, Si, Zhenjie
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 field is much smaller or much larger than the tangential velocity field,
Externí odkaz:
http://arxiv.org/abs/2405.09726
Autor:
Bian, Dongfen, Grenier, Emmanuel
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 asymptotic behaviour of solutions to the linearized incompressible Eul
Externí odkaz:
http://arxiv.org/abs/2403.13549
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 $\bb{T}\times\bb{R}$. We establish the upper and lower bounds of the linearized soluti
Externí odkaz:
http://arxiv.org/abs/2401.17102
Autor:
Bian, Dongfen, Grenier, Emmanuel
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 generic shear layers are nonlinearly unstable provided the Reynolds number
Externí odkaz:
http://arxiv.org/abs/2401.15679
Autor:
Bian, Dongfen, Grenier, Emmanuel
This article gathers notes of two lectures given at Grenoble's University in June $2023$, and is an introduction to recent works on shear layers, in collaboration with D. Bian, Y. Guo, T. Nguyen and B. Pausader.
Externí odkaz:
http://arxiv.org/abs/2312.16955
Autor:
Bian, Dongfen, Grenier, Emmanuel
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 for small horizontal Fourier variable $\alpha$, when the viscosity $\nu
Externí odkaz:
http://arxiv.org/abs/2312.16938
Autor:
Bian, Dongfen, Grenier, Emmanuel
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 limit of Navier Stokes equations in a bounded domain as the viscosity g
Externí odkaz:
http://arxiv.org/abs/2206.01318
Autor:
Bian, Dongfen, Grenier, Emmanuel
Publikováno v:
Science China Mathematics, 2023
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 presentation of the study of Orr Sommerfeld equation and to detail th
Externí odkaz:
http://arxiv.org/abs/2205.12001