TH
Thomas Y. Hou
math.APcs.NAmath.NAcs.ITmath.ITcs.LGcs.CEinstantaneous frequencymath.MPmath-ph
On Valency
published · living versionsW_b3c4g9dh·v1 · currentpublished
Nonuniqueness of the D Euler Evolutions with Vorticity
with Xiang Qin, Peicong Song, Wenhan Zhang
1 version
W_u4vamxpp·v1published
Preprints & journals
67 papers in the corpus · 2006–2026Self-Similar Solutions of the 2D Incompressible Euler Equations via a Lagrangian Construction2610.25783v1 · Thomas Y. Hou, Xiang Qin, Peicong Song et al.2026 · 0 citationsarXivon Valency
On the Stability of Type II Blowup for the Keller-Segel System in High Dimensions2609.16467v1 · Thomas Y. Hou, Xiang Qin, Peicong Song et al.2026 · 0 citationsarXiv
Analytic finite-rank corrections for singularly weighted estimates in a computer-assisted proof of 3D Euler singularity2607.15256v1 · Jiajie Chen, Thomas Y. Hou2026 · 0 citationsarXiv
Exact Blowup Analysis for the Weak-Advection Hou--Li Model2606.26658v1 · Thomas Y. Hou, Xiang Qin, Xiuyuan Wang2026 · 0 citationsarXiv
Forward Self-Similar Solutions to the 2D Hypodissipative Navier-Stokes Equations2603.12497v2 · Thomas Y. Hou, Peicong Song2026 · 0 citationsarXiv
Self-similar blow-up profile for the one-dimensional reduction of generalized SQG with infinite energy2603.11301v1 · Thomas Y. Hou, Xiang Qin, Yannick Sire et al.2026 · 0 citationsarXiv
Singularity formation in 3D Euler equations with smooth initial data and boundary.40577113 · Chen, Jiajie, Hou, Thomas Y2025 · 4 citationsProceedings of the National Academy of Sciences of the United States of America. 2025;122(27):e2500940122
High precision PINNs in unbounded domains: application to singularity formulation in PDEs2506.19243v1 · Yixuan Wang, Ziming Liu, Zongyi Li et al.2025 · 1 citationarXiv
Axisymmetric type II blowup solutions to the three-dimensional Keller-Segel system2502.19775v3 · Thomas Y. Hou, Van Tien Nguyen, Peicong Song2025 · 0 citationsarXiv
On the stability of blowup solutions to the complex Ginzburg-Landau equation in R^d2407.15812v1 · Jiajie Chen, Thomas Y. Hou, Van Tien Nguyen et al.2024 · 0 citationsarXiv
Nearly self-similar blowup of generalized axisymmetric Navier-Stokes equations2405.10916v3 · Thomas Y. Hou2024 · 0 citationsarXiv
KAN: Kolmogorov-Arnold Networks2404.19756v5 · Ziming Liu, Yixuan Wang, Sachin Vaidya et al.2024 · 852 citationsarXiv
-based stability of blowup with log correction for semilinear heat equation2404.09410v2 · Thomas Y. Hou, Van Tien Nguyen, Yixuan Wang2024 · 0 citationsarXiv
Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier-Stokes2306.04146v2 · Thomas Y. Hou, Yixuan Wang2023 · 5 citationsarXiv
Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data II: Rigorous Numerics2305.05660v3 · Jiajie Chen, Thomas Y. Hou2023 · 24 citationsarXiv
Potential Singularity of the Axisymmetric Euler Equations with Initial Vorticity for A Large Range of 2212.11912v2 · Thomas Y. Hou, Shumao Zhang2022 · 0 citationsarXiv
Potential Singularity of the Axisymmetric Euler Equations with Initial Vorticity for A Large Range of . Part II: the -Dimensional Case2212.11924v2 · Thomas Y. Hou, Shumao Zhang2022 · 0 citationsarXiv
Exponentially Convergent Multiscale Finite Element Method2212.00823v2 · Yifan Chen, Thomas Y. Hou, Yixuan Wang2022 · 4 citationsarXiv
FC-PINO: High Precision Physics-Informed Neural Operators via Fourier Continuation2211.15960v4 · Adarsh Ganeshram, Valentin Duruisseaux, Haydn Maust et al.2022 · 6 citationsarXiv
Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data I: Analysis2210.07191v4 · Jiajie Chen, Thomas Y. Hou2022 · 5 citationsarXiv
On stability and instability of singular solutions to the 3D Euler and 2D Boussinesq equations2206.01296v1 · Jiajie Chen, Thomas Y. Hou2022 · 3 citationsarXiv
The potentially singular behavior of the 3D Navier-Stokes equations2107.06509v2 · Thomas Y. Hou2021 · 1 citationarXiv
Potential singularity of the 3D Euler equations in the interior domain2107.05870v2 · Thomas Y. Hou2021 · 16 citationsarXiv
Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations2106.05422v2 · Jiajie Chen, Thomas Y. Hou, De Huang2021 · 22 citationsarXiv
Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference2105.05489v1 · Shumao Zhang, Pengchuan Zhang, Thomas Y. Hou2021 · 1 citationarXiv
Exponentially convergent multiscale methods for high frequency heterogeneous Helmholtz equations2105.04080v4 · Yifan Chen, Thomas Y. Hou, Yixuan Wang2021 · 2 citationsarXiv
Potential singularity formation of incompressible axisymmetric Euler equations with degenerate viscosity coefficients2102.06663v3 · Thomas Y. Hou, De Huang2021 · 6 citationsarXiv
Multiscale Elliptic PDEs Upscaling and Function Approximation via Subsampled Data2010.04199v2 · Yifan Chen, Thomas Y. Hou2020 · 2 citationsarXiv
Function Approximation via The Subsampled Poincaré Inequality1912.08173v3 · Yifan Chen, Thomas Y. Hou2019 · 1 citationPublished in Discrete and Continuous Dynamical Systems A, 2020
Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization1911.12518v2 · Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang2019 · 3 citationsarXiv
A class of robust numerical methods for solving dynamical systems with multiple time scales1909.04289v1 · Thomas Y. Hou, Zhongjian Wang, Zhiwen Zhang2019 · 1 citationarXiv
A model reduction method for multiscale elliptic PDEs with random coefficients using an optimization approach1807.02394v1 · Thomas Y. Hou, Dingjiong Ma, Zhiwen Zhang2018 · 19 citationsarXiv
A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition1804.03415v2 · Thomas Y. Hou, De Huang, Ka Chun Lam et al.2018 · 8 citationsarXiv
Global regularity for a family of 3D models of the axisymmetric Navier-Stokes equations1708.07536v1 · Thomas Y Hou, Pengfei Liu, Fei Wang2017 · 5 citationsarXiv
Sparse operator compression of higher-order elliptic operators with rough coefficients1708.02701v1 · Thomas Y. Hou, Pengchuan Zhang2017 · 58 citationsarXiv
An adaptive fast solver for a general class of positive definite matrices via energy decomposition1707.08277v3 · Thomas Y. Hou, D. Huang, K.C. Lam et al.2017 · 43 citationsarXiv
On the non-uniqueness of the instantaneous frequency1607.02548v2 · Peyman Tavallali, Thomas Y. Hou2016 · 0 citationsarXiv
Exploring the locally low dimensional structure in solving random elliptic PDEs1607.00693v2 · Thomas Y. Hou, Qin Li, Pengchuan Zhang2016 · 21 citationsarXiv
A sparse decomposition of low rank symmetric positive semi-definite matrices1607.00702v2 · Thomas Y. Hou, Qin Li, Pengchuan Zhang2016 · 9 citationsarXiv
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods1604.08312v1 · Eric Chung, Yalchin Efendiev, Thomas Y. Hou2016 · 193 citationsarXiv
Sparse time-frequency decomposition based on dictionary adaptation.26953172 · Hou, Thomas Y, Shi, Zuoqiang2016 · 23 citationsPhilosophical transactions. Series A, Mathematical, physical, and engineering sciences. 2016;374(2065):20150192
Extracting a shape function for a signal with intra-wave frequency modulation.26953176 · Hou, Thomas Y, Shi, Zuoqiang2016 · 35 citationsPhilosophical transactions. Series A, Mathematical, physical, and engineering sciences. 2016;374(2065):20150194
Adaptive data analysis: theory and applications.26953179 · Huang, Norden E, Daubechies, Ingrid, Hou, Thomas Y2016 · 5 citationsPhilosophical transactions. Series A, Mathematical, physical, and engineering sciences. 2016;374(2065):20150207
On the convergence and accuracy of the cardiovascular intrinsic frequency method.27019733 · Tavallali, Peyman, Hou, Thomas Y, Rinderknecht, Derek G et al.2016 · 22 citationsRoyal Society open science. 2015;2(12):150475
Optimal Local Multi-scale Basis Functions for Linear Elliptic Equations with Rough Coefficient1508.00346v1 · Thomas Y. Hou, Pengfei Liu2015 · 2 citationsarXiv
Sparse Time-Frequency decomposition for multiple signals with same frequencies1507.02037v1 · Thomas Y. Hou, Zuoqiang Shi2015 · 4 citationsarXiv
A Heterogeneous Stochastic FEM Framework for Elliptic PDEs1409.3619v1 · Thomas Y. Hou, Pengfei Liu2014 · 10 citationsarXiv
Intrinsic frequency for a systems approach to haemodynamic waveform analysis with clinical applications.25008087 · Pahlevan, Niema M, Tavallali, Peyman, Rinderknecht, Derek G et al.2015 · 44 citationsJournal of the Royal Society, Interface. 2014;11(98):20140617
Potentially singular solutions of the 3D axisymmetric Euler equations.25157172 · Luo, Guo, Hou, Thomas Y2015 · 151 citationsProceedings of the National Academy of Sciences of the United States of America. 2014;111(36):12968-73
Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations1407.5740v2 · Thomas Y. Hou, Pengfei Liu2014 · 20 citationsarXiv
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