7 citations · 20 across the 8 of their papers we have counts for
10 papers
Nonlinear stability of 3-D plane Couette flow for Boussinesq system in a finite channel
Jinkai Li, Zhilin Lin, Dong Wang
In this paper, we study the hydrodynamics stability of the 3-D plane Couette flow with constant temperature state for the Boussinesq system in a finite channel…
Stability for the 2-D plane Poiseuille flow in finite channel
Shijin Ding, Zhilin Lin
In this paper, we study the stability for 2-D plane Poiseuille flow in a channel with Navier-slip boundary condition. We prove that if the ini…
Well-posedness of Navier-Stokes/Cahn-Hilliard equations modeling the dynamics of contact line in a channel
Shijin Ding, Yinghua Li, Zhilin Lin +1
In this paper, we study the contact line problem in a channel. Precisely, we consider the incompressible Navier-Stokes/Cahn-Hilliard system with eneralized Navier boundary conditio…
Nonlinear stability for 3-D plane Poiseuille flow in a finite channel
Qi Chen, Shijin Ding, Zhilin Lin +1
In this paper, we study the nonlinear stability for the 3-D plane Poiseuille flow at high Reynolds number in a finite channel $\mathbb{T}\times [-1,1 ]\times \ma…
Stability of the boundary layer expansion for the 3D plane parallel MHD flow
Shijin Ding, Zhilin Lin, Dongjuan Niu
In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flows of viscous incompressible magnetohydrodynam…
Validity of Prandtl layer theory for steady magnetohydrodynamics over a moving plate with nonshear outer ideal MHD flows
Shijin Ding, Zhijun Ji, Zhilin Lin
In this paper, we validate the boundary layer theory for 2D steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain u…
Enhanced dissipation and transition threshold for the 2-D plane Poiseuille flow via resolvent estimate
Shijin Ding, Zhilin Lin
In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Poiseuille flow in a finite channel with Navier-slip boundary co…
Verification of Prandtl boundary layer ansatz for the steady electrically conducting fluids with a moving physical boundary
Shijin Ding, Zhilin Lin, Feng Xie
In this paper, we are concerned with the validity of Prandtl boundary layer expansion for the solutions to two dimensional (2D) steady viscous incompressible magnetohydrodynamics (…
Boundary layer for 3D plane parallel channel flows of nonhomogeneous incompressible Navier-Stokes equations
Shijin Ding, Zhilin Lin, Dongjuan Niu
In this paper, we establish the mathematical validity of the Prandtl boundary layer theory for a class of nonlinear plane parallel flow of nonhomogeneous incompressible Navier-Stok…
Stability for two-dimensional plane Couette flow to the incompressible Navier-Stokes equations with Navier boundary conditions
Shijin Ding, Zhilin Lin
This paper concerns with the stability of the plane Couette flow resulted from the motions of boundaries that the top boundary and the bottom one move with constant vel…