相关论文: Transition threshold for the 2-D Couette flow in a…
In this paper, we investigate the transition threshold problem concerning the 2-D Navier-Stokes equations in the context of Couette flow $(y,0)$ at high Reynolds number $Re$ in whole space. By utilizing Green's function estimates for the…
In this paper, we study nonlinear stability of the 3D plane Couette flow $(y,0,0)$ at high Reynolds number ${Re}$ in a finite channel $\mathbb{T}\times [-1,1]\times \mathbb{T}$. It is well known that the plane Couette flow is linearly…
In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Poiseuille flow $(1-y^2,0)$ in a finite channel with Navier-slip boundary condition. Based on the resolvent estimates for the linearized…
In this paper, we study the transition threshold of the 3D Couette flow in Sobolev space at high Reynolds number $\text{Re}$. It was proved that if the initial velocity $v_0$ satisfies $\|v_0-(y,0,0)\|_{H^2}\le c_0\text{Re}^{-1}$, then the…
We investigate the stability of the 2-D Navier-Stokes equations in the infinite channel $\mathbb{R}\times [-1,1]$ with the Navier-slip boundary condition. We show that if the initial perturbations $\omega^{in}$ around the Couette flow…
The transition mechanism from laminar flow to turbulent flow is a central problem in hydrodynamic stability theory. To shed light on this transition mechanism, Trefethen et al.({\it \small Science 1993}) proposed the transition threshold…
In this paper, we develop a stability threshold theorem for the 2D incompressible Navier-Stokes equations on the channel, supplemented with the no-slip boundary condition. The initial datum is close to the Couette flow in the following…
In this paper, we consider the stability threshold of the 2D shear flow $(U(y),0)^{\top}$ of the Navier-Stokes equation at high Reynolds number $Re$. When the shear flow is near in Sobolev norm to the Couette flow $(y,0)^{\top}$ in some…
We study the stability threshold of the 2D Couette flow in Sobolev spaces at high Reynolds number $Re$. We prove that if the initial vorticity $\Omega_{in}$ satisfies $\|\Omega_{in}-(-1)\|_{H^{\sigma}}\leq \epsilon Re^{-1/3}$, then the…
In this paper, we investigate the nonlinear stability of the Couette flow for the two-dimensional compressible Navier--Stokes equations at high Reynolds numbers ($Re$) regime. It was proved that if the initial data $(\rho_{in},u_{in})$…
We study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number $\textbf{Re}$. We prove that for sufficiently regular initial data of size $\epsilon \leq…
We consider the 2D Navier-Stokes equation on $\mathbb T \times \mathbb R$, with initial datum that is $\varepsilon$-close in $H^N$ to a shear flow $(U(y),0)$, where $\| U(y) - y\|_{H^{N+4}} \ll 1$ and $N>1$. We prove that if $\varepsilon…
Rotation significantly influences the stability characteristics of both laminar and turbulent shear flows. This study examines the stability threshold of the three-dimensional Navier-Stokes equations with rotation, in the vicinity of the…
In this work, we prove a threshold theorem for the 2D Navier-Stokes equations posed on the periodic channel, $\mathbb{T} \times [-1,1]$, supplemented with Navier boundary conditions $\omega|_{y = \pm 1} = 0$. Initial datum is taken to be a…
This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number $\textbf{Re}$. In this work, we show that there is constant $0…
We study Sobolev regularity disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number $\textbf{Re}$. Our goal is to estimate how the stability threshold scales in…
We prove a stability threshold theorem for 2D Navier-Stokes on three unbounded domains: the whole plane $\mathbb{R} \times \mathbb{R}$, the half plane $\mathbb{R} \times [0,\infty)$ with Navier boundary conditions, and the infinite channel…
We study the nonlinear stability of the two-dimensional Navier-Stokes equations around the Couette shear flow in the channel domain $\mathbb{R}\times[-1,1]$ subject to Navier slip boundary conditions. We establish a quantitative stability…
In this paper, we study the stability threshold of the two-dimensional Boussinesq equations around the Couette flow in an infinite channel $\mathbb{R} \times [-1, 1]$ under no-slip boundary conditions. We prove that the Couette flow is…
In this paper, we investigate the quantitative stability for the 2D Couette flow on the infinite channel $\mathbb{R}\times [-1,1]$ with non-slip boundary condition. Compared to the case $\mathbb{T}\times [-1,1]$, we establish the stability…