Xinyu Cheng

Xinyu Cheng

PDE/Analysis/Numerics

Research Interest

My interest is on the mathematical analysis of PDEs and applied mathematics including interfacial change, free boundary and fluid models. This is my research statement.

Publications and preprints (by year)

published

  1. On the Spectral Gap of a Square Distance Matrix, joint with D. Li, D. Shirokoff and B. Wetton, J. Stat. Phys., 2017, 166(3-4), 1029–1035. pdf

  2. Asymptotic Behaviour of Time Stepping Methods for Phase Field Models, joint with D. Li, K. Promislow and B. Wetton, J. Sci. Comput., 2021, 86(3), 1–34. pdf

  3. On a parabolic Sine-Gordon model, joint with D. Li, C. Quan and W. Yang, Numerical Mathematics: Theory, Methods and Applications., 2021, 14(4), 1068–1084.pdf

  4. Non-uniqueness of stationary weak solutions to the surface quasi-geostrophic equations, joint with H. Kwon and D. Li, Comm. Math. Phys., 2021, 388 (3), 1281-1295.pdf

  5. Global wellposedness for 2D quasilinear wave without Lorentz, joint with D. Li, J. Xu and D. Zha, Dynam. Part. Differ. Eq., 2022, 19(2) , 123-140. pdf

  6. On the equivalence of classical Helmholtz equation and fractional Helmholtz equation with arbitrary order, joint with D. Li and W. Yang , to appear in Comm. Contemp. Math.pdf

  7. Equivalent formulations of the oxygen diffusion problem and other implicit free boundary value problems and implications for numerical approximation, joint with Z. Fu and B. Wetton, SIAM J. Appl. Math., 2023, 83(1), 52-78.pdf

  8. On the global well-posedness and scattering of the 3D Klein-Gordon-Zakharov system, joint with J. Xu, Calc. Var. Part. Differ. Eqn., 63(17), 2024. pdf

  9. Localization for general Helmholtz, joint with D. Li and W. Yang, J. Diff. Eqn., 393: 139-154, 2024. pdf

preprints

  1. Unconditionally stable exponential integrator schemes for the 2D Cahn-Hilliard equation, arXiv:2312.15656.

  2. Energy stable semi-implicit schemes for the 2D Allen-Cahn and fractional Cahn-Hilliard equations, [preprint].

  3. Energy stable semi-implicit schemes for the 3D Allen-Cahn equation, [preprint].

  4. Second order energy stable semi-implicit schemes for the 2D Allen-Cahn equation, [preprint].

  5. On a Sinc-type MBE model, joint with D. Li, C. Quan and W. Yang, submitted, arXiv:2106.16193.

  6. Uniform Boundedness of Highest Norm for 2D Quasilinear Wave, joint with D. Li and J. Xu, submitted, arXiv:2104.10019.

  7. Energy stability and convergence of Strang splitting method for Cahn-Hilliard equation, joint with D. Li, preprint.

  8. Global well-posedness for 2D quasilinear wave equations with non-compactly supported initial data, joint with D. Li and J. Xu, preprint.

  9. Global well-posedness of a two dimensional wave-Klein-Gordon system with small non-compactly supported data, arXiv:2312.00821.

  10. On semi-implicit schemes for the incompressible Euler equations via the vanishing viscosity limit, joint with Z. Luo and S. Wang, arXiv:2406.12320.

  11. Global well-posedness and uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model, joint with Z. Luo, Z. Yang and C. Yuan, arXiv:2410.09340.

Academic activities

conferences and talks

  • 第四届国际生物数学建模、分析与应用研讨会 @ Harbin Engineering University 2024/06

  • 非线性分析青年学术研讨会 @ Wuhan University of Technology 2024/06

  • 三亚波国际前沿论坛@清华三亚国际数学论坛 2024/01

  • “面向未来的复杂系统科学–交叉与融合”学者讲习班 @ IICS, Fudan University 2023/11

  • Seminar talk @ Institute of Mathematical Sciences, ShangTech University 2023/11

  • Seminar talk @ School of Mathematics, South China University of Technology 2023/07

  • CSIAM 2022 @ Guangzhou, Guangdong, China 2022/09

  • Workshop on Analysis and PDE @ Tianjin Center for Applied Mathematics (TCAM) 2019/08

  • SIAM Conference on Applications of Dynamical Systems @ Snowbird, UT, US 2019/05

visiting

  • South China University of Technology, Guangzhou, China 2023/06-2023/07

  • SUSTech, Shenzhen, China 2021/10-2022/01

  • SUSTech, Shenzhen, China 2021/02-2021/04

  • Tianjin University, Tianjin, China 2019/06-2019/07

  • SUSTech, Shenzhen, China 2018/07

  • Michigan State University, East Lansing, US 2018/04

referee work

  • I have refereed articles for publications in Classical and Quantum Gravity, Physica Scripta, IMA Journal of Numerical Analysis, Advances in Computational Mathematics, Fractional Calculus and Applied Analysis, Dynamics of Partial Differential Equations.