1. On the exact self-similar finite-time blowup of the Hou-Luo model with smooth profiles
           De Huang, Xiang Qin, Xiuyuan Wang, and Dongyi  Wei.
           Communications in Mathematical Physics, 406(243), 2025.  [  .pdf    |    journal    |    arXiv math.AP 2308.01528  ]
   
   

2. Multi-scale self-similar finite-time blowups of the Constantin-Lax-Majda model for the 3D Euler equations
   De Huang, Xiang Qin, Xiuyuan Wang.
   SIAM Journal on Mathematical Analysis, 57(4), 2025.  [  .pdf    |    journal    |    arXiv math.AP 2401.14615  ]
   
   

3. Steady contiguous vortex-patch dipole solutions of the 2D incompressible Euler equation
   De Huang, Jiajun Tong.
   Archive for Rational Mechanics and Analysis, 249(46), 2025.  [  .pdf/.pdf   |    journal    |    arXiv math.AP 2406.09849 ]
   
   

4. Self-similar finite-time blowups with smooth profiles of the generalized Constantin-Lax-Majda model
   De Huang, Xiang Qin, Xiuyuan Wang, and Dongyi  Wei.
   Archive for Rational Mechanics and Analysis, 248(2): 22, 2024. [  .pdf    |    journal    |    arXiv math.AP 2305.05895  ] 
   ( I highly recommend you read the arXiv version v5. The ARMA version has a  very strange type setting and some typos: the display of some equations are really messed up. ) 

5. On self-similar finite-time blowups of the De Gregorio model on the real line
   De Huang, Jiajun Tong, and Dongyi Wei
   Communications in Mathematical Physics, 402: 2791–2829, 2023. [  .pdf    |    journal    |  arXiv math.AP  2209.08232 ]
   
   

6. Potential singularity formation of incompressible axisymmetric Euler equations with degenerate viscosity coefficients
   Thomas Y. Hou and De Huang.
   Multiscale Modeling & Simulation, 21(1), 2023. [  .pdf    |    journal    |    arXiv math.AP 2102.06663  ]
   
   

7. Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations
   Jiajie Chen, Thomas Y. Hou, and De Huang.
   Annals of PDE, 8, 24, 2022. [  .pdf    |    journal    |   arXiv math.AP 2106.05422 ]
   
   

8. A potential two-scale traveling wave singularity for 3D incompressible Euler equations
         Thomas Y. Hou and De Huang.
           Physica D: Nonlinear Phenomena, 133257, 2022.  [  .pdf    |    journal  ]
   
   

9. Matrix concentration for products
   De Huang, Jonathan Niles-Weed, Joel A. Tropp, and Rachel Ward.
   Foundations of Computational Mathematics, 13: 1-33, 2021. [  .pdf    |    journal    |    arXiv math.PR 2003.05437  ]
   
   

10. Streaming k-PCA: Efficient guarantees for Oja’s algorithm, beyond rank-one updates
    De Huang, Jonathan Niles-Weed, and Rachel Ward.
    In Conference on Learning Theory, pp. 2463-2498, PMLR, 2021. [  .pdf    |    conference    |    arXiv cs.DS 2102.03646  ]
    
    

11. From Poincaré inequalities to nonlinear matrix concentration
    De Huang and Joel A. Tropp.
    Bernoulli, 27(3): 1724-1744, 2021. [  .pdf    |    journal    |    arXiv math.PR 2006.16561 ]
    
    

12. On the finite-time blowup of the De Gregorio model for the 3D Euler equations
    Jiajie Chen, Thomas Y. Hou, and De Huang.

Communications on Pure and Applied Mathematics, 74(6): 1282-1350, 2021. [  .pdf    |    journal    |    arXiv math.AP 2905.06387]

13. Nonlinear matrix concentration via semigroup methods
    De Huang and Joel A. Tropp.
    Electronic Journal of Probability, 26: 1-31, 2020. [  .pdf    |    journal    |    arXiv math.PR 2006.16562  ]
    
    

14. Generalizing Lieb’s concavity theorem via operator interpolation
    De Huang.
    Advances in Mathematics, 369: 107208, 2020. [  .pdf    |    journal    |    arXiv math.FA 1904.03304  ]
    
    

15. A generalized Lieb’s theorem and its applications to spectrum estimates for a sum of random matrices
    De Huang.
    Linear Algebra and its Applications, 579: 419-448, 2019. [  .pdf    |    journal    |    arXiv math.ST 1808.05550  ]
    
    

16. A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition
    Thomas Y. Hou, De Huang, Ka Chun Lam, and Ziyun Zhang.
    Multiscale Modeling & Simulation, 17(1): 260-306, 2019. [  .pdf    |    journal    |    arXiv math.NA 1804.03415  ]
    
    

17. An adaptive fast solver for a general class of positive definite matrices via energy decomposition
    Thomas Y. Hou, De Huang, Ka Chun Lam, and Pengchuan Zhang.
    Multiscale Modeling & Simulation, 16(2): 615-678, 2018. [  .pdf    |    journal    |    arXiv math.NA 1707.08277  ]

1. Bernstein-type inequalities for Markov chains and Markov processes: A simple and robust proof
   De Huang, Xiangyuan Li.
   Submitted to Bernoulli, 2024.  [  .pdf    |    arXiv math.PR 2408.04930 ]
   
   

2. Non-asymptotic estimates for Markov transition matrices with rigorous error bounds
   De Huang, Xiangyuan Li.
   Submitted to Electronic Journal of Probability,  2024.  [  .pdf    |    arXiv math.PR 2408.05963 ]

1. Positive Definite Matrices: Compression, Decomposition, Eigensolver, and Concentration

D. Huang.

Ph.D. dissertation, Applied and Computational Mathematics, Caltech, 2020. [  .pdf  ]
Advisor: T. Y. Hou.

1. Generality of Lieb's concavity theorem
   D. Huang.
   [  .pdf    |    arXiv math.FA 1906.00002  ]

1. Numerical Approaches towards Incompressible Fluid Singularity
   21st NSNMF,  Aug  2025.
   
   

2. Self-similar Finite-time Blowups of the 3D Incompressible Euler Equations and Related Models
   Workshop on mixing, enhanced dissipation, and stability effects in fluid dynamics, Nov 2024.
   
   

3. Potential Multi-scale Self-similar Finite-time Blowups of the 3D Incompressible Euler Equations
   Workshop on Singularity Formations in Incompressible Fluid Flows, Westlake University, Jun 2024.
   
   

4. Potential Multi-scale Self-similar Finite-time Blowups of the 3D Incompressible Euler Equations
   Recent Developments in Applied Mathematics and its Applications, Chinese University of Hong Kong, May 2024.
   
   

5. Potential Multi-scale Self-similar Finite-time Blowups of the 3D Incompressible Euler Equations
   Analysis in fluids, dynamics, and waves, Fuzhou University, Apr 2024.
   
   

6. Exact self-similar finite-time blowups of some 1D models for the incompressible Euler equations
   Workshop on Mathematical Fluid Dynamics, Westlake University, Oct 2023.
   
   

7. Self-similar finite-time blouwps of the De Gregorio model on the real line
   Chinese Mathematical Society Annual Conference, Feb 2023.
   
   

8. Potential Singularity Formation of the 3D Axisymmetric Euler Equations with vanishing numerical viscosity
   Workshop on dissipated system,  Duke Kunshan University, May 2021.
   
   

9. Products of Random Matrices
   Conference on Applied Linear Algebra, Random Matrices and Numerical Linear Algebra, SIAM online conference, May 2021.
   
   

10. Potential Singularity Formation of the 3D Euler Equations and Related Models
    Workshop on Scientific Computing and Optimization, University of Hong Kong, Dec. 2020.
    
    

11. Generalized Lieb’s Concavity Theorems and Applications to Random Matrices
    Machine Learning for Multiscale Model Reduction Workshop, Center of Mathematical Sciences and Application, Harvard University, Mar. 2019.
    
    

12. A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition
    Southern California Applied Mathematics Symposium, California Institute of Technology, Apr. 2019.
    
    

13. Energy Decomposition with Applications to Operator Compression and Multiresolution Matrix Decomposition
    Multiscale Problems in Materials Science and Biology Analysis and Computation Workshop, Tsinghua Sanya International Mathematics Forum, Jan. 2018.