Career • 2025.05- present, Associate Professor, ShanghaiTech University • 2021.08- 2025.05, Assistant Professor, ShanghaiTech University • 2018.09-2021.05, Assistant Professor（NTT）, University of Southern California Education • 2012.09-2018.09, Ph.D in Mathematics, University of Massachusetts Amherst • 2008.09-2012.09, B.S. in Mathematics, University of Science and Technology of China Research Interest My research interests include Nonlinear dispersive PDEs in both deterministic and probabilistic settings. Selected Publications [1] On well-posedness results for the cubic-quintic NLS on T^3 (with Y. Luo, X. Yu and Z. Zhao). Nonlinear Anal. 257, 113806 (2025). [2] 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. [3] 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. [4] 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. [5] 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. [6] 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). [7] 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. [8] 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. [9] Random tensors, propagation of randomness, and nonlinear dispersive equations (with Y. Deng and A. R. Nahmod). Invent. math. 228, (2022): 539--686. Slides. [10] 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. [11] 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. [12] Global well-posedness for the energy-critical focusing nonlinear Schrödinger equation on T^4. J. Differential Equations, 280 (2021): 754--804. [13] Almost surely well-posedness for the cubic nonlinear Schrödinger equation in the supercritical regime on T^d, d>=3. Stoch. Partial Differ. Equ. Anal. Comput. 9, (2021): 243--294. [14] Global well-posedness for the focusing cubic NLS on the product space R × T^3 (with X. Yu and Z. Zhao). SIAM J. Math. Anal. 53, no. 2 (2021): 2243--2274. [15] Almost sure existence of global weak solutions to the Boussinesq equations (with W. Wang). Dyn. Partial Differ. Equ. 17, no. 2, (2020): 165--183. [16] 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. |
Email: yuehaitian@shanghaitech.edu.cn Office: S514, School of Creativity & Arts Personal Website: https://sites.google.com/view/yuehaitian |
