27 citations · 39 across the 18 of their papers we have counts for
7 papers · 1 filter
On the global well-posedness and scattering of the 3D Klein-Gordon-Zakharov system
Xinyu Cheng, Jiao Xu
In this paper we are interested in the global well-posedness of the 3D Klein-Gordon-Zakharov equations with small initial data. We show the uniform boundedness of the energy for th…
Localization for general Helmholtz
Xinyu Cheng, Dong Li, Wen Yang
In \cite{gmw2022}, Guan, Murugan and Wei established the equivalence of the classical Helmholtz equation with a ``fractional Helmholtz" equation in which the Laplacian operator is…
On a parabolic sine-Gordon model
Xinyu Cheng, Dong Li, Chaoyu Quan +1
We consider a parabolic sine-Gordon model with periodic boundary conditions. We prove a fundamental maximum principle which gives a priori uniform control of the solution. In the o…
Global wellposedness for 2D quasilinear wave without Lorentz
Xinyu Cheng, Dong Li, Jiao Xu +1
We consider the two-dimensional quasilinear wave equations with standard null-form type quadratic nonlinearities. We prove global wellposedness without using the Lorentz boost vect…
Uniform boundedness of highest norm for 2D quasilinear wave
Xinyu Cheng, Dong Li, Jiao Xu
We consider the two-dimensional quasilinear wave equations with quadratic nonlinearities. We introduce a new class of null forms and prove uniform boundedness of the highest order…
Equivalent formulations of the oxygen depletion problem, other implicit free boundary value problems, and implications for numerical approximation
Xinyu Cheng, Zhaohui Fu, Brian Wetton
The Oxygen Depletion problem is an implicit free boundary value problem. The dynamics allow topological changes in the free boundary. We show several mathematical formulations of t…
Non-uniqueness of steady-state weak solutions to the surface quasi-geostrophic equations
Xinyu Cheng, Hyunju Kwon, Dong Li
We show the existence of nontrivial stationary weak solutions to the surface quasi-geostrophic equations on the two dimensional periodic torus.