Research

Alazard, T., Shao, C. (2023). KAM via Standard Fixed Point Theorems. arXiv preprint, arXiv:2312.13971

Shao, C. (2023). On the Cauchy Problem of Spherical Capillary Water Waves. arXiv preprint, arXiv:2310.07113

Shao, C. (2023). Toolbox of Para-differential Calculus on Compact Lie Groups. arXiv preprint, arXiv:2310.06806 

Shao, C. (2022). Longtime Dynamics of Irrotational Spherical Water Drops: Initial Notes. arXiv preprint, arXiv:2301.00115

Shao, C. (2022). Long Time Dynamics of Spherical Objects Governed by Surface Tension, Doctoral dissertation, Massachusetts Institute of Technology. The final version can be found here: Chengyang Shao Thesis.pdf 

Shao, C. (2022) Long Time Behavior of a Quasilinear Hyperbolic System Modelling Elastic Membranes. Arch Rational Mech Ana, 243(2), 501-557. https://doi.org/10.1007/s00205-021-01730-8 

Heller, G., Shao, C. (2021) Strichartz and Multi-linear Estimates for 1D Periodic Dysthe Equation. arXiv preprint, arXiv:2112.12734 . This is the MIT PRIMES research paper for year 2021.

Shao, C. (2018). Schauder Type Estimates for a Class of Hypoelliptic Operators. arXiv Preprint, https://arxiv.org/abs/1805.12283

Shao, C. (2017). On the convergence of massive harmonic explorers to mSLE(4) curves. This is my undergraduate thesis under the supervision of Professor Dmitry Chelkak. A version can be found here. Dmitry Chelkak and Yijun Wan cited this work as unpublished in the following paper: Chelkak, D., & Wan, Y. (2021). On the convergence of massive loop-erased random walks to massive SLE (2) curves. Electronic Journal of Probability, 26, 1-35.