104 citations · 392 across the 34 of their papers we have counts for
31 papers · 1 filter
Collapse of white dwarfs above the Chandrasekhar mass
Gong Chen, Zhiwu Lin
We give a dynamical characterization of the Chandrasekhar mass for cold white dwarfs governed by the radial Euler--Poisson equations with the exact Chandrasekhar equation of state.…
On the nonlinear instability of nonrotating Stars
Zhiwu Lin, Xinlin Wu
We study radial nonlinear instability of compactly supported nonrotating equilibria of the three-dimensional Euler--Poisson system with a physical-vacuum boundary. Let den…
Unstable Manifolds of Stratified Euler Equations
Zhiwu Lin, Yanbo Wang, Chongchun Zeng
We consider a spectrally unstable steady state of the incompressible stratified Euler equations on a class of -dimensional domains. Assuming that the linearized equa…
Expanding solutions near unstable Lane-Emden stars
Ming Cheng, Xing Cheng, Zhiwu Lin
We consider the compressible Euler-Poisson equations for polytropes with and the white dwarf stars. For we…
Nonlinear stability of non-rotating gaseous stars
Zhiwu Lin, Yucong Wang, Hao Zhu
For the non-rotating gaseous stars modeled by the compressible Euler-Poisson system with general pressure law, Lin and Zeng [18] proved a turning point principle, which gives the s…
On the stability and instability of Kelvin-Stuart cat's-eye flows
Shasha Liao, Zhiwu Lin, Hao Zhu
Kelvin-Stuart vortices are classical mixing layer flows with many applications in fluid mechanics, plasma physics and astrophysics. We prove that the whole family of Kelvin-Stuart…
Turning point principle for stability of viscous gaseous stars
Ming Cheng, Zhiwu Lin, Yucong Wang
We consider stability of non-rotating viscous gaseous stars modeled by the Navier-Stokes-Poisson system. Under general assumptions on the equations of states, we proved that the nu…
Stability of rotating gaseous stars
Zhiwu Lin, Yucong Wang
We consider stability of rotating gaseous stars modeled by the Euler-Poisson system with general equation of states. When the angular velocity of the star is Rayleigh stable, we pr…
Prandtl-Batchelor flows on a disk
Mingwen Fei, Chen Gao, Zhiwu Lin +1
For steady two-dimensional flows with a single eddy (i.e. nested closed streamlines), Prandtl (1905) and Batchelor (1956) proposed that in the limit of vanishing viscosity the vort…
Prandtl-Batchelor flows on an annulus
Mingwen Fei, Chen Gao, Zhiwu Lin +1
For steady two-dimensional Navier-Stokes flows with a single eddy (i.e. nested closed streamlines) in a simply connected domain, Prandtl (1905) and Batchelor (1956) found that in t…
Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach
Zhiwu Lin
We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwell systems for collisionless plasmas. The linearized systems can be written as separable Hamiltonian syst…
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…
Separable Hamiltonian PDEs and Turning point principle for stability of gaseous stars
Zhiwu Lin, Chongchun Zeng
We consider stability of non-rotating gaseous stars modeled by the Euler-Poisson system. Under general assumptions on the equation of states, we proved a turning point principle (T…
Dynamics near the solitary waves of the supercritical gKDV Equations
Jiayin Jin, Zhiwu Lin, Chongchun Zeng
This work is devoted to study the dynamics of the supercritical gKDV equations near solitary waves in the energy space . We construct smooth local center-stable, center-unstab…
Barotropic instability of shear flows
Zhiwu Lin, Jincheng Yang, Hao Zhu
We consider barotropic instability of shear flows for incompressible fluids with Coriolis effects. For a class of shear flows, we develop a new method to find the sharp stability c…
Invariant Manifolds of traveling waves of the 3D Gross-Pitaevskii equation in the energy space
Jiayin Jin, Zhiwu Lin, Chongchun Zeng
We study the local dynamics near general unstable traveling waves of the 3D Gross-Pitaevskii equation in the energy space by constructing smooth local invariant center-stable, cent…
Metastability of Kolmogorov flows and inviscid damping of shear flows
Zhiwu Lin, Ming Xu
First, we consider Kolmogorov flow (a shear flow with a sinusoidal velocity profile) for 2D Navier-Stokes equation on a torus. Such flows, also called bar states, have been numeric…
Nonlinear Modulational Instability of Dispersive PDE Models
Jiayin Jin, Shasha Liao, Zhiwu Lin
We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations…
Instability, index theorem, and exponential trichotomy for Linear Hamiltonian PDEs
Zhiwu Lin, Chongchun Zeng
Consider a general linear Hamiltonian system in a Hilbert space . We assume that induces a bounded and symmetric bi-linear form $\left\lang…
Linear Inviscid Damping for Couette Flow in Stratified Fluid
Jincheng Yang, Zhiwu Lin
We study the inviscid damping of Couette flow with an exponentially stratified density. The optimal decay rates of the velocity field and the density are obtained for general pertu…
The existence of stable BGK waves
Yan Guo, Zhiwu Lin
The 1D Vlasov-Poisson system is the simplest kinetic model for describing an electrostatic collisonless plasma, and the BGK waves are its famous exact steady solutions. They play a…
Stability of traveling waves of nonlinear Schrödinger equation with nonzero condition at infinity
Zhiwu Lin, Zhengping Wang, Chongchun Zeng
We study the stability of traveling waves of nonlinear Schrödinger equation with nonzero condition at infinity obtained via a constrained variational approach. Two important physic…
Unstable manifolds of Euler equations
Zhiwu Lin, Chongchun Zeng
We consider a steady state of the Euler equation in a fixed bounded domain in . Suppose the linearized Euler equation has an exponential dichotomy of unstab…
Samll BGK waves and nonlinear Landau damping (higher dimensions)
Zhiwu Lin, Chongchun Zeng
Consider Vlasov-Poisson system with a fixed ion background and periodic condition on the space variables, in any dimension d\geq2. First, we show that for general homogeneous equil…