104 citations · 392 across the 34 of their papers we have counts for
4 papers · 2 filters
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…