Author

Xiao-Ping Zhai

3 papers indexed here

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Preprint Sep 2026

Enhanced dissipation and stability threshold for the Navier--Stokes equations near Poiseuille flow

We study the nonlinear stability of the quadratic plane Poiseuille flow $U(y)=(y^2,0)$ for the two-dimensional incompressible Navier--Stokes equations on $\mathbb T\times\mathbb R$. We prove that for initial perturbations of size $O(\nu^{2/3})$ in a $\nu$-dependent weighted Sobolev space, the flow is globally nonlinear...

Tao Liang, Cui-Li Zhai, Xiao-Ping Zhai · 0 citations

Preprint Sep 2026

Linear Growth and Nonlinear Stability of Two-Dimensional MHD Couette Flow with Vertical Dissipation

We study the two-dimensional incompressible magnetohydrodynamic system near the Couette equilibrium $\bigl((y,0)^{\rm T},(\beta,0)^{\rm T}\bigr)$ on $\mathbb T\times\mathbb R$, in the anisotropic regime where both viscosity and magnetic diffusivity act only in the vertical direction. For the inviscid linearized problem...

Tao Liang, Jia-Hong Wu, Xiao-Ping Zhai · 1 citation

Preprint Sep 2026

Sharp linear stability and the absence of enhanced dissipation for Kolmogorov flow in the 2D Navier--Stokes equations with horizontal dissipation

We study the linearized dynamics of the Kolmogorov flow $U^{(0)}=(a\sin x_2,0)$ for the two-dimensional incompressible Navier--Stokes equations with horizontal dissipation $\nu\partial_1^2$. Unlike the fully dissipative case, this anisotropic system admits $U^{(0)}$ as an exact unforced steady state. On each horizontal...

Wan-Rong Yang, Jia-Hong Wu, Xiao-Ping Zhai · 0 citations