(orcid 0000-0001-6287-1133)
Hou, Thomas Y.; Zhang, Shumao (2022) Potential Singularity of the Axisymmetric Euler Equations with C^α Initial Vorticity for A Large Range of α. Part I: the 3-Dimensional Case arXiv; https://doi.org/10.48550/arXiv.2212.11912
Hou, Thomas Y.; Zhang, Shumao (2022) Potential Singularity of the Axisymmetric Euler Equations with C^α Initial Vorticity for A Large Range of α. Part II: the N-Dimensional Case arXiv; https://doi.org/10.48550/arXiv.2212.11924
Chen, Yifan; Hou, Thomas Y. et al. (2022) Exponentially Convergent Multiscale Finite Element Method arXiv; https://doi.org/10.48550/arXiv.2212.00823
Maust, Haydn; Li, Zongyi et al. (2022) Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators arXiv; https://doi.org/10.48550/arXiv.2211.15960
Chen, Jiajie; Hou, Thomas Y. (2022) Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data arXiv; https://doi.org/10.48550/arXiv.2210.07191
Chen, Jiajie; Hou, Thomas Y. (2022) On stability and instability of C^(1,α) singular solutions to the 3D Euler and 2D Boussinesq equations arXiv; https://doi.org/10.48550/arXiv.2206.01296
Hou, Thomas Y.; Li, Zhenzhen et al. (2021) Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold arXiv; https://doi.org/10.48550/arXiv.2107.09207
Hou, Thomas Y. (2021) The potentially singular behavior of the 3D Navier-Stokes equations arXiv; https://doi.org/10.48550/arXiv.2107.06509
Hou, Thomas Y. (2021) Potential singularity of the 3D Euler equations in the interior domain arXiv; https://doi.org/10.48550/arXiv.2107.05870
Hou, Thomas Y.; Li, Zhenzhen et al. (2020) Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization arXiv; https://doi.org/10.48550/arXiv.2012.15467
Hou, Thomas Y.; Li, Zhenzhen et al. (2019) Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization arXiv; https://doi.org/10.48550/arXiv.1911.12518
Hou, Thomas Y.; Wang, Zhongjian et al. (2019) A class of robust numerical methods for solving dynamical systems with multiple time scales arXiv; https://doi.org/10.48550/arXiv.1909.04289
Choi, Kyudong; Hou, Thomas Y. et al. (2015) On the Finite-Time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations https://doi.org/10.48550/arXiv.1407.4776
Hou, Thomas Y.; Shi, Zuoqiang (2015) Sparse Time-Frequency decomposition for multiple signals with same frequencies https://doi.org/10.48550/arXiv.1507.02037 (Submitted)
Hou, Thomas Y.; Liu, Pengfei (2015) Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations https://doi.org/10.48550/arXiv.1407.5740 (Submitted)
Hou, Thomas Y.; Luo, Guo (2013) On the Finite-Time Blowup of a 1D Model for the 3D Incompressible Euler Equations https://doi.org/10.48550/arXiv.1311.2613 (Submitted)
Hou, Thomas Y.; Shi, Zuoqiang et al. (2011) On the Local Well-posedness of a 3D Model for Incompressible Navier-Stokes Equations with Partial Viscosity https://doi.org/10.48550/arXiv.1107.1823 (Submitted)
Deng, J.; Hou, T. Y. et al. (2006) Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation https://doi.org/10.48550/arXiv.0601427 (Submitted)