Research Interests
Research Interests
Partial differential equations (primary): Fluid dynamics, Navier-Stokes equations, Euler equations, singularity formation, self-similar solutions, dynamic rescaling method
Matrix analysis: positive definite matrices, trace inequalities, Lieb's concavity theorem, operator interpolation
Random matrix theory: matrix concentration inequalities, Markov process, matrix martingale
Declaration: None of my research works listed below have utilized or relied on any AI models or resources.
If I ever conduct research using or relying on AI in the future, the resulting papers will be exhibited on a separate page.
Uniformly rotating vortex patches with 90-degree corners
De Huang, Jiajun Tong, and Xiaopeng Zheng.
Preprint. [ arXiv math.AP 2608.13134 ]
Steady contiguous vortex-patch dipole solutions of the 2D incompressible Euler equation
De Huang and Jiajun Tong.
Archive for Rational Mechanics and Analysis, 249(4), 46, 2025. [ .pdf/.pdf | journal | arXiv math.AP 2406.09849 ]
Novel self-similar finite-time blowups with singular profiles of the 1D Hou-Luo model and the 2D Boussinesq equations: A numerical investigation
Bojin Chen, De Huang, and Xiangyuan Li.
Preprint. [ arXiv math.AP 2604.01868 ]
Self-similar finite-time blowups with singular profiles of the generalized Constantin-Lax-Majda model: theoretical and numerical investigations
De Huang, Jiajun Tong, and Xiuyuan Wang.
Nonlinearity, 39(9): 095005, 2026. [ .pdf | journal | arXiv math.AP 2603.25104 ]
(Note: After the paper was published in Nonlinearity, we realized that some important properties of traveling-wave solutions, though established in Section 7, were missing in the main Theorem 2.7, and a formal proof of Theorem 2.7 was also missing. We addressed these issues in the newest arXiv version (v4). So if you are interested in this paper, please read its arXiv version math.AP 2603.25104, which is more informative and complete.)
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(10), 243, 2025. [ .pdf | journal | arXiv math.AP 2308.01528 ]
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): 4068-4096, 2025. [ .pdf | journal | arXiv math.AP 2401.14615 ]
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 ]
(Note: 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. )
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(3): 2791-2829, 2023. [ .pdf | journal | arXiv math.AP 2209.08232 ]
Potential singularity formation of incompressible axisymmetric Euler equations with degenerate viscosity coefficients
Thomas Y. Hou and De Huang.
Multiscale Modeling & Simulation, 21(1): 218-268, 2023. [ .pdf | journal | arXiv math.AP 2102.06663 ]
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(2), 24, 2022. [ .pdf | journal | arXiv math.AP 2106.05422 ]
A potential two-scale traveling wave singularity for 3D incompressible Euler equations
Thomas Y. Hou and De Huang.
Physica D: Nonlinear Phenomena, 435, 133257, 2022. [ .pdf | journal ]
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 ]
Bernstein-type inequalities for Markov chains and Markov processes: A simple and robust proof
De Huang and Xiangyuan Li.
Bernoulli, 32(2): 1267-1284, 2026. [ .pdf | journal | arXiv math.PR 2408.04930 ]
Non-asymptotic estimates for Markov transition matrices via spectral gap methods
De Huang and Xiangyuan Li.
Electronic Journal of Probability, 30: 1-28, 2025. [ .pdf | journal | arXiv math.PR 2408.05963 ]
Matrix concentration for products
De Huang, Jonathan Niles-Weed, Joel A. Tropp, and Rachel Ward.
Foundations of Computational Mathematics, 22(6): 1767-1799, 2022. [ .pdf | journal | arXiv math.PR 2003.05437 ]
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, PMLR, 134: 2463-2498, 2021. [ .pdf | conference | arXiv cs.DS 2102.03646 ]
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 ]
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 ]
Generality of Lieb's concavity theorem
De Huang.
Manuscript. [ .pdf | arXiv math.FA 1906.00002 ]
Generalizing Lieb’s concavity theorem via operator interpolation
De Huang.
Advances in Mathematics, 369, 107208, 2020. [ .pdf | journal | arXiv math.FA 1904.03304 ]
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 ]
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 ]
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 ]
Uniformly rotating vortex patches with 90-degree corners
De Huang, Jiajun Tong, and Xiaopeng Zheng.
[ arXiv math.AP 2608.13134 ]
Novel self-similar finite-time blowups with singular profiles of the 1D Hou-Luo model and the 2D Boussinesq equations: A numerical investigation
Bojin Chen, De Huang, and Xiangyuan Li.
[ arXiv math.AP 2604.01868 ]
Self-similar finite-time blowups with singular profiles of the generalized Constantin-Lax-Majda model: theoretical and numerical investigations
De Huang, Jiajun Tong, and Xiuyuan Wang.
Nonlinearity, 39(9): 095005, 2026. [ .pdf | journal | arXiv math.AP 2603.25104 ]
(Note: After the paper was published in Nonlinearity, we realized that some important properties of traveling-wave solutions, though established in Section 7, were missing in the main Theorem 2.7, and a formal proof of Theorem 2.7 was also missing. We addressed these issues in the newest arXiv version (v4). So if you are interested in this paper, please read its arXiv version math.AP 2603.25104, which is more informative and complete.)
Bernstein-type inequalities for Markov chains and Markov processes: A simple and robust proof
De Huang and Xiangyuan Li.
Bernoulli, 32(2): 1267-1284, 2026. [ .pdf | journal | arXiv math.PR 2408.04930 ]
Non-asymptotic estimates for Markov transition matrices via spectral gap methods
De Huang and Xiangyuan Li.
Electronic Journal of Probability, 30: 1-28, 2025. [ .pdf | journal | arXiv math.PR 2408.05963 ]
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(10), 243, 2025. [ .pdf | journal | arXiv math.AP 2308.01528 ]
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): 4068-4096, 2025. [ .pdf | journal | arXiv math.AP 2401.14615 ]
Steady contiguous vortex-patch dipole solutions of the 2D incompressible Euler equation
De Huang and Jiajun Tong.
Archive for Rational Mechanics and Analysis, 249(4), 46, 2025. [ .pdf/.pdf | journal | arXiv math.AP 2406.09849 ]
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 ]
(Note: 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. )
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(3): 2791-2829, 2023. [ .pdf | journal | arXiv math.AP 2209.08232 ]
Potential singularity formation of incompressible axisymmetric Euler equations with degenerate viscosity coefficients
Thomas Y. Hou and De Huang.
Multiscale Modeling & Simulation, 21(1): 218-268, 2023. [ .pdf | journal | arXiv math.AP 2102.06663 ]
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(2), 24, 2022. [ .pdf | journal | arXiv math.AP 2106.05422 ]
A potential two-scale traveling wave singularity for 3D incompressible Euler equations
Thomas Y. Hou and De Huang.
Physica D: Nonlinear Phenomena, 435, 133257, 2022. [ .pdf | journal ]
Matrix concentration for products
De Huang, Jonathan Niles-Weed, Joel A. Tropp, and Rachel Ward.
Foundations of Computational Mathematics, 22(6): 1767-1799, 2022. [ .pdf | journal | arXiv math.PR 2003.05437 ]
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, PMLR, 134: 2463-2498, 2021. [ .pdf | conference | arXiv cs.DS 2102.03646 ]
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 ]
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]
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 ]
Generalizing Lieb’s concavity theorem via operator interpolation
De Huang.
Advances in Mathematics, 369, 107208, 2020. [ .pdf | journal | arXiv math.FA 1904.03304 ]
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 ]
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 ]
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 ]
Positive Definite Matrices: Compression, Decomposition, Eigensolver, and Concentration
De Huang.
Ph.D. dissertation, Applied and Computational Mathematics, Caltech, 2020. [ .pdf ]
Advisor: T. Y. Hou.
Generality of Lieb's concavity theorem
De Huang.
[ .pdf | arXiv math.FA 1906.00002 ]