27 citations · 39 across the 18 of their papers we have counts for
18 papers
Some inequalities and gradient estimates for harmonic functions on Finsler measure spaces
Xinyue Cheng, Yalu Feng
In this paper, we study functional and geometric inequalities on complete Finsler measure spaces under the condition that the weighted Ricci curvature has a lowe…
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…
The characterizations on a class of weakly weighted Einstein-Finsler metrics
Xinyue Cheng, Hong Cheng, Pengsheng Wu
In this paper, we study the weakly weighted Einstein-Finsler metrics. First, we show that weakly weighted Einstein-Kropina metrics must be of isotropic S-curvature with respect to…
Some inequalities on Finsler manifolds with weighted Ricci curvature bounded below
Xinyue Cheng, Zhongmin Shen
We establish some important inequalities under a lower weighted Ricci curvature bound on Finsler manifolds. Firstly, we establish a relative volume comparison of Bishop-Gromov type…
On a sinc-type MBE model
Xinyu Cheng, Dong Li, Chaoyu Quan +1
We introduce a new sinc-type molecular beam epitaxy model which is derived from a cosine-type energy functional. The landscape of the new functional is remarkably similar to the cl…
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…
Some important applications of improved Bochner inequality on Finsler manifolds
Xinyue Cheng
We establish some important inequalities under the condition that the weighted Ricci curvature for some constant by using improved Bochner ineq…
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.
The navigation problems and the curvature properties on conic Kropina manifolds
Xinyue Cheng, Qiuhong Qu, Suiyun Xu
In this paper, we study navigation problems on conic Kropina manifolds. Let be a conic Kropina metric on an -dimensional manifold and be a conformal vector fie…
The Randers metrics of weakly isotropic scalar curvature
Xinyue Cheng, Yannian Gong
In this paper, we study the Randers metrics of weakly isotropic scalar curvature. We prove that a Randers metric of weakly isotropic scalar curvature must be of isotropic -curva…
Some fundamental problems in global Finsler geometry
Xinyue Cheng
The geometry and analysis on Finsler manifolds is a very important part of Finsler geometry. In this article, we introduce some important and fundamental topics in global Finsler g…
Asymptotic Behaviour of Time Stepping Methods for Phase Field Models
Xinyu Cheng, Dong Li, Keith Promislow +1
Adaptive time stepping methods for metastable dynamics of the Allen Cahn and Cahn Hilliard equations are investigated in the spatially continuous, semi-discrete setting. We analyse…
A class of Randers metrics of scalar flag curvature
Xinyue Cheng, Li Yin, Tingting Li
One of the most important problems in Finsler geometry is to classify Finsler metrics of scalar flag curvature. In this paper, we study the classification problem of Randers metric…
Einstein Finsler Metrics and Killing Vector Fields on Riemannian Manifolds
Xinyue Cheng, Zhongmin Shen
In this paper, we use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In par…