12 papers · 1 filter
Enhanced dissipation and stability threshold for the Navier--Stokes equations near Poiseuille flow
Tao Liang, Cuili Zhai, Xiaoping Zhai
We study the nonlinear stability of the quadratic plane Poiseuille flow for the two-dimensional incompressible Navier--Stokes equations on …
Sharp linear stability and the absence of enhanced dissipation for Kolmogorov flow in the 2D Navier--Stokes equations with horizontal dissipation
Wanrong Yang, Jiahong Wu, Xiaoping Zhai
We study the linearized dynamics of the Kolmogorov flow for the two-dimensional incompressible Navier--Stokes equations with horizontal dissipation $ν\parti…
Linear Growth and Nonlinear Stability of Two-Dimensional MHD Couette Flow with Vertical Dissipation
Tao Liang, Jiahong Wu, Xiaoping Zhai
We study the two-dimensional incompressible magnetohydrodynamic system near the Couette equilibrium on , in the…
Stabilization by a background magnetic field: global well-posedness of the compressible isentropic ideal MHD equations with velocity damping
Liening Qiao, Jiahong Wu, Fuyi Xu +1
We study the Cauchy problem for the three-dimensional isentropic compressible ideal (inviscid and non-resistive) magnetohydrodynamic equations with velocity damping on the periodic…
Stability threshold of the 2D Boussinesq system near Couette flow in an infinite channel
Tao Liang, Jiahong Wu, Xiaoping Zhai
In this paper, we study the stability threshold of the two-dimensional Boussinesq equations around the Couette flow in an infinite channel under no-slip…
Improved stability threshold for 2D Navier-Stokes Couette flow in an infinite channel
Tao Liang, Jiahong Wu, Xiaoping Zhai
We study the nonlinear stability of the two-dimensional Navier-Stokes equations around the Couette shear flow in the channel domain subject to Navier slip…
Magnetic Stabilization of Compressible Flows: Global Existence in 3D Inviscid Non-Isentropic MHD Equations
Jiahong Wu, Fuyi Xu, Xiaoping Zhai
Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an…
Global solutions to 3D compressible MHD equations with partial magnetic diffusion
Jiahong Wu, Xiaoping Zhai
The global existence of strong solutions to the compressible viscous magnetohydrodynamic (MHD) equations in remains a significant open problem. When there is no magn…
Large global solutions to the Oldroyd-B model with dissipation
Tao Liang, Yongsheng Li, Xiaoping Zhai
In the first part of this work, we investigate the Cauchy problem for the -dimensional incompressible Oldroyd-B model with dissipation in the stress tensor equation. By developi…
Global well-posedness and large time behavior of solutions to the compressible Oldroyd-B model without stress diffusion
Yajuan Zhao, Yongsheng Li, Tao Liang +1
We consider the Cauchy problem () and the initial boundary values problem ()associated to the compressible Oldroyd-B model which is first…
Stability for the -D compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow
Xiaoping Zhai, Yongsheng Li, Yajuan Zhao
In this paper, we are concerned with the initial boundary values problem associated to the compressible viscous non-resistive and heat-conducting magnetohydrodynamic flow, where th…
Global well-posedness and large-time behavior for a special D full compressible viscous non-resistive MHD system
Xiaoping Zhai, Shunhang Zhang
In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertic…