16 citations · 29 across the 12 of their papers we have counts for
14 papers
Quantitative lower bound for Pythagorean pairs in boxes of prime powers
Rongzhong Xiao
For each positive integer , let be the -th prime for , and set Write $f(…
Generically sharp decay and blowing up at infinity for a weak null wave system
Shijie Dong, Siyuan Ma, Yue Ma +1
We study a system of semilinear wave equations satisfying the weak null condition, which can be regarded as a simplified model for the Einstein vacuum equations. The main objective…
Quantitative observability for one-dimensional Schrödinger equations with potentials
Pei Su, Chenmin Sun, Xu Yuan
In this note, we prove the quantitative observability with an explicit control cost for the 1D Schrödinger equation over with real-valued, bounded continuous potentia…
Generically sharp decay for quasilinear wave equations with null condition
Shijie Dong, Siyuan Ma, Yue Ma +1
We are interested in the three-dimensional quasilinear wave equations with null condition. Global existence and pointwise decay for this model have been proved in the celebrated wo…
Global solution to the 3D Dirac--Klein-Gordon system with uniform energy bounds
Shijie Dong, Kuijie Li, Xu Yuan
On the (1+3) dimensional Minkowski spacetime, for small, regular initial data, it is well-known that the Dirac-Klein-Gordon system admits a global solution. In the present paper, w…
Global Behavior of Small Data Solutions for The 2D Dirac-Klein-Gordon Equations
Shijie Dong, Kuijie Li, Yue Ma +1
In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data sol…
Asymptotic behavior of 2D Wave-Klein-Gordon coupled system under null condition
Shijie Dong, Yue Ma, Xu Yuan
We study the 2D coupled wave-Klein-Gordon systems with semi-linear null nonlinearities and . The main result states that the solution to the 2D coupled systems exists…
Construction of excited multi-solitons for the focusing 4D cubic wave equation
Xu Yuan
Consider the focusing 4D cubic wave equation \[ \partial_{tt}u-Δu-u^{3}=0,\quad \mbox{on}\ (t,x)\in [0,\infty)\times \mathbb{R}^{4}.\] The main result states the existence in energ…
Asymptotics of solutions with a compactness property for the nonlinear damped Klein-Gordon equation
Raphaël Côte, Xu Yuan
We consider the nonlinear damped Klein-Gordon equation \[ \partial_{tt}u+2α\partial_{t}u-Δu+u-|u|^{p-1}u=0 \quad \text{on} \ \ [0,\infty)\times \mathbb{R}^N \] with , $2 \le N…
Construction of excited multi-solitons for the 5D energy-critical wave equation
Xu Yuan
For the 5D energy-critical wave equation, we construct excited -solitons with collinear speeds, i.e. solutions of the equation such that \begin{equation*} \lim_{t\to+\infty}…
Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity
Xu Yuan
We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearity \begin{equation*} \partial_{t}^{2}u-\partial_{x}^{2}u+u-|u|^{p-…
Long-time asymptotics of the one-dimensional damped nonlinear Klein-Gordon equation
Raphaël Côte, Yvan Martel, Xu Yuan
For the one-dimensional nonlinear damped Klein-Gordon equation \[ \partial_{t}^{2}u+2α\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad \mbox{on ,}\]…
Description and classification of 2-solitary waves for nonlinear damped Klein-Gordon equations
Raphaël Côte, Yvan Martel, Xu Yuan +1
We describe completely 2-solitary waves related to the ground state of the nonlinear damped Klein-Gordon equation \begin{equation*} \partial_{tt}u+2α\partial_{t}u-Δu+u-|u|^{p-1}u=0…
On multi-solitons for the energy-critical wave equation in dimension 5
Xu Yuan
In this paper, we construct -solitons of the focusing energy-critical nonlinear wave equation in five-dimensional space, i.e. solutions of the equation such that \begin{equa…