24 citations · 83 across the 20 of their papers we have counts for
23 papers
Global dynamics of a supercritical wave equation in a large data regime
Shijie Dong, Zoe Wyatt, Jingya Zhao
We prove the existence of global solutions to the nonlinear wave equation in in the energy-supercritical regime , for a cl…
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…
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…
Superintegrability on the Dunkl oscillator model in three-Dimensional spaces of constant curvature
Shi-Hai Dong, Amene Najafizade, Hossein Panahi +2
This paper has studied the three-dimensional Dunkl oscillator models in a generalization of superintegrable Euclidean Hamiltonian systems to curved ones. These models are defined b…
Global solution to the cubic Dirac equation in two space dimensions
Shijie Dong, Kuijie Li
We are interested in the cubic Dirac equation with mass in two space dimensions, which is also known as the Soler model. We conduct a thorough study on this model wi…
Global Existence and Scattering of the Klein-Gordon-Zakharov System in Two Space Dimensions
Shijie Dong, Yue Ma
We are interested in the Klein-Gordon-Zakharov system in , which is an important model in plasma physics with extensive mathematical studies. The system can be re…
Asymptotic stability for the Dirac--Klein-Gordon system in two space dimensions
Shijie Dong, Zoe Wyatt
We study the Dirac--Klein-Gordon system in spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance…
The top-order energy of quasilinear wave equations in two space dimensions is uniformly bounded
Shijie Dong, Philippe G. LeFloch, Zhen Lei
Alinhac solved a long-standing open problem in 2001 and established that quasilinear wave equations in two space dimensions with quadratic null nonlinearities admit global-in-time…
Stability of some two dimensional wave maps: a wave--Klein-Gordon model
Shijie Dong, Zoe Wyatt
We are interested in the stability of a class of totally geodesic wave maps, as recently studied by Abbrescia and Chen, and later by Duan and Ma. The relevant equations of motion a…
Global solution to the Klein-Gordon-Zakharov equations with uniform energy bounds
Shijie Dong
We are interested in the Klein-Gordon-Zakharov equations in , and we aim to show that the energy for the global solution to the equations is uniformly bounded, an…
Two dimensional wave--Klein-Gordon equations with semilinear nonlinearities
Shijie Dong, Zoe Wyatt
From the work on the weak-null condition by Lindblad and Rodnianski, it is well-known that `bad' quadratic sourcing terms are allowed to appear in coupled semilinear wave equations…
Asymptotic Behavior of the Solution to the Klein-Gordon-Zakharov Model in Dimension Two
Shijie Dong
Consider the Klein-Gordon-Zakharov equations in , and we are interested in establishing the small global solution to the equations and in investigating the pointw…
Global solution to the wave and Klein-Gordon system under null condition in dimension two
Shijie Dong
We are interested in studying the coupled wave and Klein-Gordon equations with null quadratic nonlinearities in . We want to establish the small data global exist…
The zero mass problem for Klein-Gordon equations: quadratic null interactions
Shijie Dong
We study in a system of nonlinearly coupled Klein-Gordon equations under null condition, with (possibly vanishing) mass varying in the interval . Our goa…
Stability of a wave and Klein-Gordon system with mixed coupling
Shijie Dong
We are interested in establishing stability results for a system of semilinear wave and Klein-Gordon equations with mixed coupling nonlinearities, that is, we consider all of the p…
Stability of a class of semilinear waves in dimension under null condition
Shijie Dong
We will show that in $\RR^{2+1}$ semilinear wave equations of the form $-\Box u = u Q(\del u; \del u)$ possess global-in-time solutions if the null condition on $Q(\del u; \del u)$…
The zero mass problem for Klein-Gordon equations
Shijie Dong
We are interested in the global solutions to a class of Klein-Gordon equations, and particularly in the unified time decay results with respect to the possibly vanishing mass param…
Global evolution of the U(1) Higgs Boson: nonlinear stability and uniform energy bounds
Shijie Dong, Philippe G. LeFloch, Zoe Wyatt
Relying on the hyperboloidal foliation method, we establish the nonlinear stability of the ground state of the standard model of electroweak interactions. This amounts to es…
The finite volume method on a Schwarzschild background
Shijie Dong, Philippe G. LeFloch
We introduce a class of nonlinear hyperbolic conservation laws on a Schwarzschild black hole background and derive several properties satisfied by (possibly weak) solutions. Next,…
Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities
Shijie Dong, Zoe Wyatt
Using the hyperboloidal foliation method, we establish stability results for a coupled wave-Klein-Gordon system with quadratic nonlinearities. In particular, we investigate quadrat…