24 citations · 83 across the 20 of their papers we have counts for
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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,…