1 citations · 1 across the 4 of their papers we have counts for
9 papers
A note on stability of Eliasson-Kuksin's KAM tori for the nonlinear Schrödinger equation
Xiaolong He, Jia Shi, Xiaoping Yuan
Eliasson and Kuksin developed a KAM approach to study the persistence of the invariant tori for nonlinear Schrödinger equation on . In this note, we improve Eliasso…
Remarks on stationary and uniformly-rotating vortex sheets: Flexibility results
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we construct new, uniformly-rotating solutions of the vortex sheet equation bifurcating from circles with constant vorticity amplitude. The proof is accomplished via…
Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity , such that it has positive vo…
On linear stability of KAM tori via the Craig-Wayne-Bourgain method
Xiaolong He, Jia Shi, Yunfeng Shi +1
In this paper, we prove the Melnikov's persistency theorem by combining the traditional Kolmogorov-Arnold-Moser (KAM) technique and the Craig-Wayne-Bourgain (CWB) method. The aim o…
Anderson Localization for Long-Range operators with Singular Potentials
Wenwen Jian, Jia Shi, Xiaoping Yuan
In this paper, we use Cartan estimate for meromorphic functions to prove Anderson localization for a class of long-range operators with singular potenials.
Anderson Localization For The Quantum Kicked Rotor Model
Jia Shi, Xiaoping Yuan
In this paper, we establish Anderson localization for the quantum kicked rotor model. More precisely, we proved that \begin{equation*} H=\tanπ\left(x_0+my_0+\frac{m(m-1)}{2}ω\right…