My research currently focuses on: random data theory, invariant Gibbs measures under the nonlinear dispersive flows, and short & long time behaviors for nonlinear dispersive equations. I am also interested in stochastic PDEs and statistical physics.
On well-posedness results for the cubic-quintic NLS on 𝕋3 (with Y. Luo, X. Yu and Z. Zhao). Nonlinear Anal. 257, 113806 (2025).
Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two (with Y. Deng and A. R. Nahmod). Ann. of Math. (2) 200, no. 2 (2024): 399--486. Slides.
Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation (with B. Bringmann, Y. Deng and A. R. Nahmod). Invent. math. (2024). https://doi.org/10.1007/s00222-024-01254-4. Slides.
On the global well-posedness for the periodic quintic nonlinear Schrödinger equation (with X. Yu). SIAM J. Math. Anal. 56, no. 2 (2024): 1851--1902.
Global well-posedness and scattering for fourth-order Schrödinger equations on waveguide manifolds (with X. Yu and Z. Zhao). SIAM J. Math. Anal. 56, no. 1 (2024): 1427--1458.
The probabilistic scaling paradigm (with Y. Deng and A. R. Nahmod). Vietnam J. Math. (Dedicated to Carlos Kenig on the occasion of his 70th birthday) 52, 1001--1015 (2024).
Singular Levy processes and dispersive effects of generalized Schrödinger equations (with Y. Sire, X. Yu and Z. Zhao). Dyn. Partial Differ. Equ. 20, No. 2 (2023): 153--178.
On the decay property of the cubic fourth-order Schrödinger equation (with X. Yu and Z. Zhao). Proc. Amer. Math. Soc. 151 (2023): 2619--2630.
Random tensors, propagation of randomness, and nonlinear dispersive equations (with Y. Deng and A. R. Nahmod). Invent. math. 228, (2022): 539--686. Slides.
Invariant Gibbs measure and global strong solutions for the Hartree NLS equation in dimension three (with Y. Deng and A. R. Nahmod). J. Math. Phys. (Special Topics: Celebrating the work of Jean Bourgain) 62, no. 3 (2021): 031514.
Optimal local well-posedness for the periodic derivative nonlinear Schrödinger equation (with Y. Deng and A. R. Nahmod). Comm. Math. Phys. 384, (2021): 1061--1107. Slides.
Global well-posedness for the energy-critical focusing nonlinear Schrödinger equation on 𝕋4. J. Differential Equations, 280 (2021): 754--804.
Almost surely well-posedness for the cubic nonlinear Schrödinger equation in the supercritical regime on 𝕋d, d≥ 3. Stoch. Partial Differ. Equ. Anal. Comput. 9, (2021): 243--294.
Global well-posedness for the focusing cubic NLS on the product space ℝ × 𝕋3 (with X. Yu and Z. Zhao). SIAM J. Math. Anal. 53, no. 2 (2021): 2243--2274.
Almost sure existence of global weak solutions to the Boussinesq equations (with W. Wang). Dyn. Partial Differ. Equ. 17, no. 2, (2020): 165--183.
Self trapping transition for a nonlinear impurity within a linear chain (with M. Molina, P. Kevrekidis, and N. Karachalios). J. Math. Phys. 55, no. 10 (2014): 102703.
The slides of the mini-course "Random dispersive PDEs" at SLMath (MSRI), October 2025.
The video of the talk "Invariant Gibbs measures for NLS and Hartree equations" at ICERM, Generic Behavior of Dispersive Solutions and Wave Turbulence, October 2021.
The slides of the mini-course "Probabilistic well-posedness for nonlinear Schrödinger equation (I)" at ICERM, October 2021.