70 citations · 233 across the 26 of their papers we have counts for
26 papers
Couette Flow with Robin Boundary Condition (I): the viscosity-independent friction
Siming He, Binqian Niu, Weiren Zhao
This article is the first paper in the series. In this series of articles, we will examine the influence of the friction factor at the solid--fluid boundary on the stability of…
Long-time behaviour of two-dimensional Navier-Stokes equations in the presence of Couette flow on the half plane
Ning Liu, Nader Masmoudi, Weiren Zhao
In this paper, we study the long-time behavior of solutions to the two-dimensional Navier-Stokes equations in the presence of Couette flow on the half plane with Navier-slip bounda…
Optimal stability threshold in lower regularity spaces for the Vlasov-Poisson-Fokker-Planck equations
Weiren Zhao, Ruizhao Zi
In this paper, we study the optimal stability threshold for the Vlasov-Poisson equation with weak Fokker-Planck collision. We prove that if the initial perturbation is of size $ν^{…
Asymptotic stability of the three-dimensional Couette flow for the Stokes-transport equation
Daniel Sinambela, Weiren Zhao, Ruizhao Zi
In this paper, we investigate the asymptotic stability of the three-dimensional Couette flow in a stratified fluid governed by the Stokes-transport equation. We observe that a simi…
Asymptotic Stability of the two-dimensional Couette flow for the Stokes-transport equation in a finite channel
Daniel Sinambela, Weiren Zhao, Ruizhao Zi
We study the Stokes-transport system in a two-dimensional channel with horizontally moving boundaries, which serves as a reduced model for oceanography and sedimentation. The densi…
Landau damping, collisionless limit, and stability threshold for the Vlasov-Poisson equation with nonlinear Fokker-Planck collisions
Jacob Bedrossian, Weiren Zhao, Ruizhao Zi
In this paper, we study the Vlasov-Poisson-Fokker-Planck (VPFP) equation with a small collision frequency , exploring the interplay between the regularity and size of p…
Asymptotic stability in the critical space of 2D monotone shear flow in the viscous fluid
Hui Li, Weiren Zhao
In this paper, we study the long-time behavior of the solutions to the two-dimensional incompressible free Navier Stokes equation (without forcing) with small viscosity , when t…
Asymptotic stability of Couette flow in a strong uniform magnetic field for the Euler-MHD system
Weiren Zhao, Ruizhao Zi
In this paper, we prove the asymptotic stability of Couette flow in a strong uniform magnetic field for the Euler-MHD system, when the perturbations are in Gevrey-, $(…
Inviscid damping of monotone shear flows for 2D inhomogeneous Euler equation with non-constant density in a finite channel
Weiren Zhao
We prove the nonlinear inviscid damping for a class of monotone shear flows with non-constant background density for the two-dimensional ideal inhomogeneous fluids in $\mathbb{T}\t…
The transition to instability for stable shear flows in inviscid fluids
Daniel Sinambela, Weiren Zhao
In this paper, we study the generation of eigenvalues of a stable monotonic shear flow under perturbations in with . More precisely, we study the Rayleigh operator $\mat…
Asymptotic stability of two-dimensional Couette flow in a viscous fluid
Hui Li, Nader Masmoudi, Weiren Zhao
In this paper, we study the nonlinear asymptotic stability of Couette flow for the two-dimensional Navier-Stokes equation with small viscosity in …
Stability threshold of the Couette flow for Navier-Stokes Boussinesq system with large Richardson number
Cuili Zhai, Weiren Zhao
In this paper, we study the nonlinear asymptotic stability of the Couette flow in the stably stratified regime, namely the Richardson number . Precisely, we prove…
A dynamical approach to the study of instability near Couette flow
Hui Li, Nader Masmoudi, Weiren Zhao
In this paper, we obtain the optimal instability threshold of the Couette flow for Navier-Stokes equations with small viscosity , when the perturbations are in the critical sp…
Asymptotic stability for two-dimensional Boussinesq systems around the Couette flow in a finite channel
Nader Masmoudi, Cuili Zhai, Weiren Zhao
In this paper, we study the asymptotic stability for the two-dimensional Navier-Stokes Boussinesq system around the Couette flow with small viscosity and small thermal diffusio…
Metastability for the dissipative quasi-geostrophic equation and the non-local enhancement
Hui Li, Weiren Zhao
In this paper, we study the metastability for the 2-D linearized dissipative quasi-geostrophic equation with small viscosity around the quasi steady state $θ_{sin}=e^{-νt}\sin…
Linear damping and depletion in flowing plasma with strong sheared magnetic fields
Han Liu, Nader Masmoudi, Cuili Zhai +1
In this paper, we study the long-time behavior of the solution for the linearized ideal MHD around sheared velocity and magnetic field under Stern stability condition. We prove tha…
Stability of Couette flow for 2D Boussinesq system without thermal diffusivity
Nader Masmoudi, Belkacem Said-Houari, Weiren Zhao
In this paper, we prove the stability of Couette flow for 2D Navier-Stokes Boussinesq system without thermal diffusivity for the initial perturbation in Gevrey-, ($1/3…
Nonlinear inviscid damping for a class of monotone shear flows in finite channel
Nader Masmoudi, Weiren Zhao
We prove the nonlinear inviscid damping for a class of monotone shear flows in for initial perturbation in Gevrey-() class with compact support. The main…
Stability threshold of the 2D Couette flow in Sobolev spaces
Nader Masmoudi, Weiren Zhao
We study the stability threshold of the 2D Couette flow in Sobolev spaces at high Reynolds number . We prove that if the initial vorticity satisfies $\|Ω_{in}-(-1)\|_{…
Enhanced dissipation for the 2D Couette flow in critical space
Nader Masmoudi, Weiren Zhao
We consider the 2D incompressible Navier-Stokes equations on , with initial vorticity that is close in to (the vorticity of…
Long time behavior of Alfvén waves in a flowing plasma: mathematical analysis on the generation of the magnetic island
Cuili Zhai, Zhifei Zhang, Weiren Zhao
In this paper, we consider the generation of magnetic island for the linearized MHD equations around the steady flowing plasma with velocity field and magnetic field…
Linear inviscid damping and enhanced dissipation for the Kolmogorov flow
Dongyi Wei, Zhifei Zhang, Weiren Zhao
In this paper, we prove the linear inviscid damping and voticity depletion phenomena for the linearized Euler equations around the Kolmogorov flow. These results confirm Bouchet an…
Linear inviscid damping and vorticity depletion for shear flows
Dongyi Wei, Zhifei Zhang, Weiren Zhao
In this paper, we prove the linear damping for the 2-D Euler equations around a class of shear flows under the assumption that the linearized operator has no embedding eigenvalues.…
Commutator Estimates for the Dirichlet-to-Neumann Map of Stokes Systems in Lipschitz Domains
Qiang Xu, Weiren Zhao, Shulin Zhou
In the paper, we establish commutator estimates for the Dirichlet-to-Neumann map of Stokes systems in Lipschitz domains. The approach is based on Dahlberg's bilinear estimates, and…