Xuecheng Wang's Homepage
About Me:
I am an associate professor (with tenure) at Yau Mathematical Sciences Center, Tsinghua University.
I was a semester postdoc (Spring, 2017) at ICERM, Brown University for the semester program "Singularities and Waves In Incompressible Fluids". Also, I was a semester postdoc (Fall, 2016) in Mathematics Department at Princeton University.
I got my Ph.D. degree from Mathematics Department at Princeton University under the supervision of Prof. Alexandru Ionescu in 2016.
Email: xuecheng@tsinghua.edu.cn
My homepage is also maintained here.
Research Interests:
My research interests are nonlinear dispersive PDEs, nonlinear wave equations, and harmonic analysis. I am mostly interested in the global regularity problem and the optimal regularity problem. Also, I enjoy learning and researching in new topics.
Please note that the published versions of the papers might be slightly different from the preprint versions.
Preprints and Publications:
23: (With A. Ionescu, B. Pausader, and K. Widmayer) Nonlinear Landau damping and wave operators in sharp Gevrey spaces, arXiv:2405.04473, preprint, 2024.
22: Global solution of 2D hyperbolic liquid crystal system for small initial data, arXiv:2403.18385, preprint (2024).
21: (With A. Ionescu, B. Pausader, and K. Widmayer) On the stability of homogeneous equilibria in the Vlasov-Poisson system on R^3, arXiv:2305.11166, preprint, Classical and Quantum Gravity, 2023, Vol. 40, 185007.
20. Global solution of 3D anisotropic wave equations with the same speed in one direction, arXiv:2303.03973 , preprint (2023).
19. Global stability of the Minkowski spacetime for the Einstein-Vlasov system, arXiv:2210.00512, preprint (2022).
18. (With A. Ionescu, B. Pausader, and K. Widmayer) Nonlinear Landau damping for the Vlasov-Poisson system in R^3: the Poisson equilibrium, arXiv:2205.04540, preprint (2022), Annals of PDE, 10, Article number: 2 (2024). 10, Article number: 2 (2024)
17. Global solution of the 3D relativistic Vlasov-Maxwell system for large data with cylindrical symmetry, arXiv:2203.01199, preprint (2022).
16. Remarks on the large data global solutions of 3D RVP system and 3D RVM system, arXiv:2203.01202, preprint (2022), Discrete and Continuous Dynamical Systems - Series A, Vol. 43, no. 10, 3796-3829, 2023.
15. Global solution of the 3D Relativistic Vlasov-Poisson system for a class of large data, arXiv:2003.14191v3, preprint (2022), Journal of Statistical Physics, 190, Art. no. 162, (2023).
The main result (2020, the radial case) in v1 is now contained and also improved to allow initial data with cylindrical symmetry in v3 (2022).
14. (With A. Ionescu, B. Pausader, and K. Widmayer), On the asymptotic behavior of solutions to the Vlasov-Poisson system,
arXiv:2005.03617, International Mathematics Research Notices, Vol. 2022, no. 12, 8865–8889.
13. Global solution of the 3D relativistic Vlasov-Maxwell system for the large radial data, arXiv:2003.14192, preprint (2020). Not for publication, the assumption on the initial data is relaxed to cylindrical symmetry in arXiv:2203.01199.
12. Decay estimates for the 3D relativistic and non-relativistic Vlasov-Poisson systems, Kinetic and Related Models, 16(2023), no 1, 1-19.
11. Propagation of regularity and long time behavior of the 3D massive relativistic transport equation II: Vlasov-Maxwell system, Communications in Mathematical Physics., 389 (2022), no. 2, 715-812.
10. Propagation of regularity and long time behavior of 3D massive relativistic transport equation I: Vlasov-Nordström system, Communications in Mathematical Physics, 382 (2021), no. 3, 1843–1934.
9. Global regularity for the 3D finite depth capillary water waves, Annales scientifiques de l’ Ecole normale superieure, 53 (2020), no. 4, 847–943.
8. Global solution for the 3D quadratic Schr\"odinger equation of $Q(u, \bar{u})$ type, Discrete and Continuous Dynamical Systems - Series A, Vol 37 (2017), no 9, 5037-5048.
7. Global solution for the 3D gravity water waves system above a flat bottom, Advances in Mathematics, Vol. 346 (2019), 805-886.
6. On the 3-dimensional water waves system above a flat bottom, Analysis & PDE, Vol. 10 (2017), No. 4, 893–928.
5. Global infinite energy solutions for the 2D gravity water waves system, Communications on Pure and Applied Mathematics, 71(2018), no. 1, 90-162.
4. Global existence for the 2D incompressible isotropic elastodynamics for small initial data, Annales Henri Poincaré , 18 (2017), no.4, 1213–1267.
3. On global existence of 3D charge critical Dirac-Klein-Gordon system, International Mathematics Research Notices, (2015) 2015 (21): 10801-10846.
2. (With Benoit Pausader and Nikolay Tzvetkov) Global regularity for the energy-critical NLS on S^3, Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 2014; 31(2), 315-338.
1. A Beurling-Hormander theorem associated with the Riemann-Liouville operator, Pacific Journal of Mathematics, 251(2011), pp 239--255.