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 below have utilized or relied on any AI models or resources.
If I ever conduct reserach using or relying on AI in the future, the resulting papers will be posted 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 ]
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 ]
( 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 ]
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 ]
( 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 ]