Hou, Thomas Y.; Wang, Yixuan Blowup analysis for a quasi-exact 1D model of 3D Euler and Navier-Stokes. (English) Zbl 07801563 Nonlinearity 37, No. 3, Article ID 035001, 28 p. (2024). MSC: 35Q30 35Q31 76D03 76D05 76B03 35B44 35C06 42A16 35A01 35A02 68V05 PDFBibTeX XMLCite \textit{T. Y. Hou} and \textit{Y. Wang}, Nonlinearity 37, No. 3, Article ID 035001, 28 p. (2024; Zbl 07801563) Full Text: DOI arXiv OA License
Hou, Thomas Y. Potential singularity of the 3D Euler equations in the interior domain. (English) Zbl 07781557 Found. Comput. Math. 23, No. 6, 2203-2249 (2023). MSC: 35Q31 35Q30 76B03 76D05 35B07 35B44 35C06 35A21 65N06 65L06 PDFBibTeX XMLCite \textit{T. Y. Hou}, Found. Comput. Math. 23, No. 6, 2203--2249 (2023; Zbl 07781557) Full Text: DOI arXiv
Hou, Thomas Y.; Huang, De Potential singularity formation of incompressible axisymmetric Euler equations with degenerate viscosity coefficients. (English) Zbl 1514.35318 Multiscale Model. Simul. 21, No. 1, 218-268 (2023). MSC: 35Q30 35Q31 35A21 PDFBibTeX XMLCite \textit{T. Y. Hou} and \textit{D. Huang}, Multiscale Model. Simul. 21, No. 1, 218--268 (2023; Zbl 1514.35318) Full Text: DOI arXiv
Chen, Jiajie; Hou, Thomas Y. Correction to: “Finite time blowup of 2D Boussinesq and 3D Euler equations with \(C^{1,\alpha}\) velocity and boundary. (English) Zbl 1511.35046 Commun. Math. Phys. 399, No. 1, 573-575 (2023). MSC: 35B44 35L65 35L67 35Q31 76B03 PDFBibTeX XMLCite \textit{J. Chen} and \textit{T. Y. Hou}, Commun. Math. Phys. 399, No. 1, 573--575 (2023; Zbl 1511.35046) Full Text: DOI
Chen, Jiajie; Hou, Thomas Y.; Huang, De Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations. (English) Zbl 1504.35247 Ann. PDE 8, No. 2, Paper No. 24, 75 p. (2022). MSC: 35Q31 76B03 76E30 35C06 35B44 35A02 PDFBibTeX XMLCite \textit{J. Chen} et al., Ann. PDE 8, No. 2, Paper No. 24, 75 p. (2022; Zbl 1504.35247) Full Text: DOI arXiv
Hou, Thomas Y.; Zhang, Shumao Potential Singularity of the Axisymmetric Euler Equations with \(C^\alpha\) Initial Vorticity for A Large Range of \(\alpha\). Part II: the \(N\)-Dimensional Case. arXiv:2212.11924 Preprint, arXiv:2212.11924 [math.AP] (2022). MSC: 35Q31 76B03 65M60 65M06 65M20 BibTeX Cite \textit{T. Y. Hou} and \textit{S. Zhang}, ``Potential Singularity of the Axisymmetric Euler Equations with $C^\alpha$ Initial Vorticity for A Large Range of $\alpha$. Part II: the $N$-Dimensional Case'', Preprint, arXiv:2212.11924 [math.AP] (2022) Full Text: arXiv OA License
Hou, Thomas Y.; Zhang, Shumao Potential Singularity of the Axisymmetric Euler Equations with \(C^\alpha\) Initial Vorticity for A Large Range of \(\alpha\). Part I: the \(3\)-Dimensional Case. arXiv:2212.11912 Preprint, arXiv:2212.11912 [math.AP] (2022). MSC: 35Q31 76B03 65M60 65M06 65M20 BibTeX Cite \textit{T. Y. Hou} and \textit{S. Zhang}, ``Potential Singularity of the Axisymmetric Euler Equations with $C^\alpha$ Initial Vorticity for A Large Range of $\alpha$. Part I: the $3$-Dimensional Case'', Preprint, arXiv:2212.11912 [math.AP] (2022) Full Text: arXiv OA License
Chen, Jiajie; Hou, Thomas Y.; Huang, De On the finite time blowup of the de Gregorio model for the 3D Euler equations. (English) Zbl 1469.35053 Commun. Pure Appl. Math. 74, No. 6, 1282-1350 (2021). MSC: 35B44 35Q31 PDFBibTeX XMLCite \textit{J. Chen} et al., Commun. Pure Appl. Math. 74, No. 6, 1282--1350 (2021; Zbl 1469.35053) Full Text: DOI arXiv Link
Chen, Jiajie; Hou, Thomas Yizhao Finite time blowup of 2D Boussinesq and 3D Euler equations with \(C^{1, \alpha}\) velocity and boundary. (English) Zbl 1485.35071 Commun. Math. Phys. 383, No. 3, 1559-1667 (2021); correction ibid. 399, No. 1, 573-575 (2023). Reviewer: Ilya A. Chernov (Petrozavodsk) MSC: 35B44 35L65 35L67 76B03 35Q31 PDFBibTeX XMLCite \textit{J. Chen} and \textit{T. Y. Hou}, Commun. Math. Phys. 383, No. 3, 1559--1667 (2021; Zbl 1485.35071) Full Text: DOI arXiv
Luo, Guo; Hou, Thomas Y. Formation of finite-time singularities in the 3D axisymmetric Euler equations: a numerics guided study. (English) Zbl 1427.35190 SIAM Rev. 61, No. 4, 793-835 (2019). MSC: 35Q31 76B03 65M60 65M06 65M20 65L06 35B44 PDFBibTeX XMLCite \textit{G. Luo} and \textit{T. Y. Hou}, SIAM Rev. 61, No. 4, 793--835 (2019; Zbl 1427.35190) Full Text: DOI
Hou, Thomas Y.; Jin, Tianling; Liu, Pengfei Potential singularity for a family of models of the axisymmetric incompressible flow. (English) Zbl 1405.35150 J. Nonlinear Sci. 28, No. 6, 2217-2247 (2018). MSC: 35Q31 35Q30 76D05 35B65 35B07 PDFBibTeX XMLCite \textit{T. Y. Hou} et al., J. Nonlinear Sci. 28, No. 6, 2217--2247 (2018; Zbl 1405.35150) Full Text: DOI
Choi, Kyudong; Hou, Thomas Y.; Kiselev, Alexander; Luo, Guo; Sverak, Vladimir; Yao, Yao On the finite-time blowup of a one-dimensional model for the three-dimensional axisymmetric Euler equations. (English) Zbl 1377.35218 Commun. Pure Appl. Math. 70, No. 11, 2218-2243 (2017). MSC: 35Q31 35B44 35B07 76B03 PDFBibTeX XMLCite \textit{K. Choi} et al., Commun. Pure Appl. Math. 70, No. 11, 2218--2243 (2017; Zbl 1377.35218) Full Text: DOI Link
Hou, Thomas Y.; Liu, Pengfei Self-similar singularity of a 1D model for the 3D axisymmetric Euler equations. (English) Zbl 1320.35269 Res. Math. Sci. 2, Paper No. 5, 26 p. (2015). MSC: 35Q31 35C06 35A20 76N10 PDFBibTeX XMLCite \textit{T. Y. Hou} and \textit{P. Liu}, Res. Math. Sci. 2, Paper No. 5, 26 p. (2015; Zbl 1320.35269) Full Text: DOI arXiv
Luo, Guo; Hou, Thomas Y. Potentially singular solutions of the 3D axisymmetric Euler equations. (English) Zbl 1431.35115 Proc. Natl. Acad. Sci. USA 111, No. 36, 12968-12973 (2014). MSC: 35Q31 35B44 35B07 76B03 PDFBibTeX XMLCite \textit{G. Luo} and \textit{T. Y. Hou}, Proc. Natl. Acad. Sci. USA 111, No. 36, 12968--12973 (2014; Zbl 1431.35115) Full Text: DOI arXiv
Luo, Guo; Hou, Thomas Y. Toward the finite-time blowup of the 3D axisymmetric Euler equations: a numerical investigation. (English) Zbl 1316.35235 Multiscale Model. Simul. 12, No. 4, 1722-1776 (2014). MSC: 35Q31 76B03 65M60 65M06 65M20 35B44 PDFBibTeX XMLCite \textit{G. Luo} and \textit{T. Y. Hou}, Multiscale Model. Simul. 12, No. 4, 1722--1776 (2014; Zbl 1316.35235) Full Text: DOI Link
Hou, Thomas Y.; Lei, Zhen; Luo, Guo; Wang, Shu; Zou, Chen On finite time singularity and global regularity of an axisymmetric model for the 3D Euler equations. (English) Zbl 1293.35228 Arch. Ration. Mech. Anal. 212, No. 2, 683-706 (2014). MSC: 35Q31 35B44 76D05 35Q30 35B65 PDFBibTeX XMLCite \textit{T. Y. Hou} et al., Arch. Ration. Mech. Anal. 212, No. 2, 683--706 (2014; Zbl 1293.35228) Full Text: DOI arXiv Link
Hou, Thomas Y.; Shi, Zuoqiang Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model. (English) Zbl 1237.76014 Discrete Contin. Dyn. Syst. 32, No. 5, 1449-1463 (2012). MSC: 76B03 35L60 35M10 PDFBibTeX XMLCite \textit{T. Y. Hou} and \textit{Z. Shi}, Discrete Contin. Dyn. Syst. 32, No. 5, 1449--1463 (2012; Zbl 1237.76014) Full Text: DOI arXiv
Hou, Thomas Y. Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations. (English) Zbl 1422.76041 Acta Numerica 18, 277-346 (2009). MSC: 76D05 35Q31 76D03 35B44 35B35 35B65 PDFBibTeX XMLCite \textit{T. Y. Hou}, Acta Numerica 18, 277--346 (2009; Zbl 1422.76041) Full Text: DOI
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei Localized non-blowup conditions for the 3D incompressible Euler equations. (English) Zbl 1172.35466 Lau, Ka-Sing (ed.) et al., Third international congress of Chinese mathematicians. Part 2. Proceedings of the ICCM ’04, Hong Kong, China, December 17–22, 2004. Providence, RI: American Mathematical Society (AMS); Somerville, MA: International Press (ISBN 978-0-8218-4452-6/pbk; 978-0-8218-4416-8/set). AMS/IP Studies in Advanced Mathematics 42, 2, 603-611 (2008). MSC: 35Q35 76B03 PDFBibTeX XMLCite \textit{J. Deng} et al., AMS/IP Stud. Adv. Math. 42, 603--611 (2008; Zbl 1172.35466)
Hou, Thomas Y.; Li, Ruo Blowup or no blowup? the interplay between theory and numerics. (English) Zbl 1143.76390 Physica D 237, No. 14-17, 1937-1944 (2008). MSC: 76B03 76M22 35Q35 PDFBibTeX XMLCite \textit{T. Y. Hou} and \textit{R. Li}, Physica D 237, No. 14--17, 1937--1944 (2008; Zbl 1143.76390) Full Text: DOI
Hou, Thomas Y.; Li, Ruo Nonexistence of locally self-similar blow-up for the 3D incompressible Navier-Stokes equations. (English) Zbl 1194.35307 Discrete Contin. Dyn. Syst. 18, No. 4, 637-642 (2007). MSC: 35Q30 35Q31 35B44 35C06 76D03 76M55 PDFBibTeX XMLCite \textit{T. Y. Hou} and \textit{R. Li}, Discrete Contin. Dyn. Syst. 18, No. 4, 637--642 (2007; Zbl 1194.35307) Full Text: DOI arXiv
Hou, Thomas Y.; Li, Ruo Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations. (English) Zbl 1370.76015 J. Nonlinear Sci. 16, No. 6, 639-664 (2006). MSC: 76B03 35B40 35L45 35Q31 76B47 76M22 PDFBibTeX XMLCite \textit{T. Y. Hou} and \textit{R. Li}, J. Nonlinear Sci. 16, No. 6, 639--664 (2006; Zbl 1370.76015) Full Text: DOI arXiv Link
Hou, Thomas Yizhao; Yang, Danping; Ran, Hongyu Multiscale computation of isotropic homogeneous turbulent flow. (English) Zbl 1119.35053 Ammari, Habib (ed.) et al., Inverse problems, multi-scale analysis and effective medium theory. Proceedings of the workshop on inverse problems, multi-scale analysis and homogenization, Seoul, Korea, June 22–24, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3968-3/pbk). Contemporary Mathematics 408, 111-135 (2006). Reviewer: Kai Schneider (Marseille) MSC: 35Q30 76F05 76M50 PDFBibTeX XMLCite \textit{T. Y. Hou} et al., Contemp. Math. 408, 111--135 (2006; Zbl 1119.35053)
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei Improved geometric conditions for non-blowup of the 3D incompressible Euler equation. (English) Zbl 1158.76305 Commun. Partial Differ. Equations 31, No. 1-3, 293-306 (2006). MSC: 76B03 35B40 35L45 35L60 35Q35 PDFBibTeX XMLCite \textit{J. Deng} et al., Commun. Partial Differ. Equations 31, No. 1--3, 293--306 (2006; Zbl 1158.76305) Full Text: DOI
Deng, Jian; Hou, Thomas Y.; Yu, Xinwei Geometric properties and nonblowup of 3D incompressible Euler flow. (English) Zbl 1142.35549 Commun. Partial Differ. Equations 30, No. 2, 225-243 (2005). MSC: 35Q35 35L60 76B03 PDFBibTeX XMLCite \textit{J. Deng} et al., Commun. Partial Differ. Equations 30, No. 2, 225--243 (2005; Zbl 1142.35549) Full Text: DOI arXiv
Ceniceros, Hector D.; Hou, Thomas Y. An efficient dynamically adaptive mesh for potentially singular solutions. (English) Zbl 0986.65087 J. Comput. Phys. 172, No. 2, 609-639 (2001). MSC: 65M50 35K55 76D17 PDFBibTeX XMLCite \textit{H. D. Ceniceros} and \textit{T. Y. Hou}, J. Comput. Phys. 172, No. 2, 609--639 (2001; Zbl 0986.65087) Full Text: DOI
Hou, Thomas Y.; Lowengrub, John S.; Shelley, Michael J. Removing the stiffness from interfacial flows with surface tension. (English) Zbl 0810.76095 J. Comput. Phys. 114, No. 2, 312-338 (1994). MSC: 76V05 76B45 76D45 76M25 76M20 PDFBibTeX XMLCite \textit{T. Y. Hou} et al., J. Comput. Phys. 114, No. 2, 312--338 (1994; Zbl 0810.76095) Full Text: DOI Link
Hou, Thomas Y. A new desingularization for vortex methods. (English) Zbl 0746.65100 Math. Comput. 58, No. 197, 103-117 (1992). Reviewer: L.G.Vulkov (Russe) MSC: 65R20 45K05 76B47 PDFBibTeX XMLCite \textit{T. Y. Hou}, Math. Comput. 58, No. 197, 103--117 (1992; Zbl 0746.65100) Full Text: DOI
Hou, Thomas Y. A survey on convergence analysis for point vortex methods. (English) Zbl 0751.76053 Vortex dynamics and vortex methods, Proc. 21st AMS-SIAM Semin., Seattle/WA (USA) 1990, Lect. Appl. Math. 28, 327-339 (1991). MSC: 76M25 76B47 76-02 PDFBibTeX XMLCite \textit{T. Y. Hou}, Lect. Appl. Math. 28, 327--339 (1991; Zbl 0751.76053)
Goodman, Jonathan; Hou, Thomas Y. New stability estimates for the 2-D vortex method. (English) Zbl 0745.76061 Commun. Pure Appl. Math. 44, No. 8-9, 1015-1031 (1991). MSC: 76M25 76B47 65N12 PDFBibTeX XMLCite \textit{J. Goodman} and \textit{T. Y. Hou}, Commun. Pure Appl. Math. 44, No. 8--9, 1015--1031 (1991; Zbl 0745.76061) Full Text: DOI
Chacon-Rebollo, Tomas; Hou, Thomas Y. A Lagrangian finite element method for the 2-D Euler equations. (English) Zbl 0705.76059 Commun. Pure Appl. Math. 43, No. 6, 735-767 (1990). MSC: 76M10 35Q30 PDFBibTeX XMLCite \textit{T. Chacon-Rebollo} and \textit{T. Y. Hou}, Commun. Pure Appl. Math. 43, No. 6, 735--767 (1990; Zbl 0705.76059) Full Text: DOI
E, Weinan; Hou, Thomas Y. Homogenization and convergence of the vortex method for 2-D Euler equations with oscillatory vorticity fields. (English) Zbl 0701.76028 Commun. Pure Appl. Math. 43, No. 7, 821-855 (1990). MSC: 76B47 35Q30 76M15 76M25 PDFBibTeX XMLCite \textit{W. E} and \textit{T. Y. Hou}, Commun. Pure Appl. Math. 43, No. 7, 821--855 (1990; Zbl 0701.76028) Full Text: DOI
Goodman, Jonathan; Hou, Thomas Y.; Lowengrub, John Convergence of the point vortex method for the 2-D Euler equations. (English) Zbl 0694.76013 Commun. Pure Appl. Math. 43, No. 3, 415-430 (1990). MSC: 76B47 35Q30 65N15 PDFBibTeX XMLCite \textit{J. Goodman} et al., Commun. Pure Appl. Math. 43, No. 3, 415--430 (1990; Zbl 0694.76013) Full Text: DOI