217 citations · 1.8k across the 81 of their papers we have counts for
77 papers · 1 filter
Neutral curves and traveling waves in plane Poiseuille flow
Hui Li, Yuxi Wang, Zhifei Zhang
We study the spectrum of the Orr--Sommerfeld operator associated with the incompressible plane Poiseuille flow in the high-Reynolds-number regime. In the Tollmien--Schlichting eige…
Zero-viscosity limit of the compressible Naiver-Stokes equations in the analytic setting
Chao Wang, Yuxi Wang, Zhifei Zhang
In this paper, we study the zero-viscosity limit of the compressible Navier-Stokes equations in a half-space with non-slip boundary condition. We justify the Prandtl boundary layer…
Tollmien-Schlichting waves in the subsonic regime
Nader Masmoudi, Yuxi Wang, Di Wu +1
The Tollmien-Schlichting (T-S) waves play a key role in the early stages of boundary layer transition. In a breakthrough work, Grenier, Guo and Nguyen gave the first rigorous const…
Nonlinear inviscid damping for 2-D inhomogeneous incompressible Euler equations
Qi Chen, Dongyi Wei, Ping Zhang +1
We prove the asymptotic stability of shear flows close to the Couette flow for the 2-D inhomogeneous incompressible Euler equations on . More precisely…
Global stability of the compressible viscous surface waves in an infinite layer
Guilong Gui, Zhifei Zhang
We investigate in this paper the global stability of the compressible viscous surface waves in the absence of surface tension effect with a steady-state violating Rayleigh-Taylor i…
Dynamic stability for steady Prandtl solutions
Yan Guo, Yue Wang, Zhifei Zhang
By establishing an invariant set (1.11) for the Prandtl equation in Crocco transformation, we prove orbital and asymptotic stability of Blasius-like steady states against Oleinik's…
Dynamics near Couette flow for the -plane equation
Luqi Wang, Zhifei Zhang, Hao Zhu
In this paper, we study stationary structures near the planar Couette flow in Sobolev spaces on a channel , and asymptotic behavior of Couette flow in Gevre…
Corrector estimates and homogenization errors of unsteady flow ruled by Darcy's law
Li Wang, Qiang Xu, Zhifei Zhang
Focusing on Darcy's law incorporating memory effects, this paper studies non-stationary Stokes equations on perforated domains. We establish a sharp homogenization error for both v…
The derivation of the compressible Euler equation from quantum many-body dynamics
Xuwen Chen, Shunlin Shen, Jiahao Wu +1
We study the three dimensional many-particle quantum dynamics in mean-field setting. We forge together the hierarchy method and the modulated energy method. We prove rigorously tha…
Asymptotic Behavior of the Steady Prandtl Equation
Yue Wang, Zhifei Zhang
We study the asymptotic behavior of the Oleinik's solution to the steady Prandtl equation when the outer flow . Serrin proved that the Oleinik's solution converges to the f…
Matrix-valued Allen-Cahn equation and the Keller-Rubinstein-Sternberg problem
Mingwen Fei, Fanghua Lin, Wei Wang +1
In this paper, we consider the sharp interface limit of a matrix-valued Allen-Cahn equation, which takes the form: $$\partial_t A=ΔA-\varepsilon^{-2}( A A^{\mathrm{T}}A- A)~~\text{…
On the stability of shear flows of Prandtl type for the steady Navier-Stokes equations
Qi Chen, Di Wu, Zhifei Zhang
In this paper, we prove the stability of shear flows of Prandtl type as for the steady Navier-Stokes equations under a natural spectral assumption on the…
Linear stability of the Couette flow in the 3D isentropic compressible Navier-Stokes equations
Lan Zeng, Zhifei Zhang, Ruizhao Zi
Consider the linear stability of the three dimensional isentropic compressible Navier-Stokes equations on . We prove the enhanced dissip…
The unconditional uniqueness for the energy-supercritical NLS
Xuwen Chen, Shunlin Shen, Zhifei Zhang
We consider the cubic and quintic nonlinear Schrödinger equations (NLS) under the and energy-supercritical setting. Via a newly developed unified…
The number of traveling wave families in a running water with Coriolis force
Zhiwu Lin, Dongyi Wei, Zhifei Zhang +1
In this paper, we study the number of traveling wave families near a shear flow under the influence of Coriolis force, where the traveling speeds lie outside the range of the flow…
Scaling invariant Serrin criterion via one velocity component for the Navier-Stokes equations
Wendong Wang, Di Wu, Zhifei Zhang
In this paper, we prove that the Leray weak solution of the Navier-Stokes equations is regular in …
Transition threshold for the 3D Couette flow in a finite channel
Qi Chen, Dongyi Wei, Zhifei Zhang
In this paper, we study nonlinear stability of the 3D plane Couette flow at high Reynolds number in a finite channel . It…
Gevrey stability of hydrostatic approximate for the Navier-Stokes equations in a thin domain
Chao Wang, Yuxi Wang, Zhifei Zhang
In this paper, we justify the limit from the Navier-Stokes system in a thin domain to the hydrostatic Navier-Stokes/Prandtl system for the convex initial data with Gevrey 9/8 regua…
On the stability of Prandtl expansions in Gevrey class
Qi Chen, Di Wu, Zhifei Zhang
In this paper, we prove the stability of Prandtl expansions of shear flow type as for the initial perturbation in the Gevrey class, whe…
Blow-up criterion for the 2-D Prandtl equation
Yue Wang, Zhifei Zhang
In this paper, we consider the 2-D Prandtl equation with constant outer flow and monotonic data. We prove that if the curvature of the velocity distribution(i.e., )…
Global Regularity of the Steady Prandtl Equation
Yue Wang, Zhifei Zhang
In this paper, we prove the global regularity of the Oleinik's solution for the steady Prandtl equation with favorable pressure.
Well-posedness of the free boundary problem in elastodynamics with mixed stability condition
Hui Li, Wei Wang, Zhifei Zhang
In this paper, we prove the local well-posedness of the free boundary problem in incompressible elastodynamics under a mixed type stability condition, i.e., for each point of the f…
Linear stability of pipe Poiseuille flow at high Reynolds number regime
Qi Chen, Dongyi Wei, Zhifei Zhang
In this paper, we prove the linear stability of the pipe Poiseuille flow for general perturbations at high Reynolds number regime. This is a long-standing problem since the experim…
Boundary layer separation and local behavior for the Steady Prandtl equation
Weiming Shen, Yue Wang, Zhifei Zhang
In the case of favorable pressure gradient, Oleinik proved the global existence of classical solution for the 2-D steady Prandtl equation for a class of positive data. In the case…