Tai-Peng Tsai: Publications
orcid 
https://orcid.org/0000-0002-9008-1136
| A. REFEREEED JOURNAL PAPERS | ||
| 1 | On Leray's self-similar solutions of the Navier-Stokes equations satisfying local energy estimates, Archive for Rational Mechanics and Analysis, 143; (1998) 29--51. | pdf erratum |
| 2 | (with V. Sverak) On the spatial decay of 3-D steady-state Navier-Stokes flows. Comm. Partial Differential Equations, 25 (2000), no. 11&12, 2107--2117. | |
| 3 | (with J. Froehlich and H.-T. Yau) On the point-particle (Newtonian) limit of the non-linear Hartree equation, Comm. Math. Phys. 225 (2002), 223-274. | |
| 4 | (with H.-T. Yau) Asymptotic dynamics of nonlinear Schrödinger equations: resonance dominated and dispersion dominated solutions, Comm. Pure Appl. Math. 55 (2002) 0153--0216. | math-ph/ 0011036 pdf |
| 5 | (with H.-T. Yau) Relaxation of excited states in nonlinear Schrödinger equations, Int. Math. Res. Not. 2002 (2002), no. 31, 1629--1673. | math-ph/ 0110009 pdf |
| 6 | (with H.-T. Yau) Stable directions for excited states of nonlinear Schrödinger equations, Comm. Partial Differential Equations 27 (2002), no. 11&12, 2363--2402. | math-ph/ 0110037 pdf |
| 7 | (with H.-T. Yau) Classification of asymptotic profiles for nonlinear Schrödinger equations with small initial data, Adv. Theor. Math. Phys. 6 (2002), no. 1, 107--139. | math-ph/ 0205015 pdf |
| 8 | (with Y. Martel and F. Merle) Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations, Comm. Math. Phys. 231 (2002) no. 2, 347--373. | math.AP/ 0112071 pdf |
| 9 | Asymptotic dynamics of nonlinear Schrödinger equations with many bound states, J. Diff. Equations 192 (2003), no 1, 225-282. | math-ph/ 0204056 |
| 10 | (with S. Gustafson and K. Nakanishi) Asymptotic stability and completeness in the energy space for nonlinear Schrödinger equations with small solitary waves, Int. Math. Res. Not., 2004 (2004) no. 66, 3559--3584. | math-ph/ 0308009 pdf |
| 11 | (with S. Gustafson and K. Kang) Regularity criteria for suitable weak solutions to the Navier-Stokes equations near the boundary, J. Diff. Equations 226 (2006) 594--618. | math.AP/ 0505190 |
| 12 | (with S. Gustafson and K. Nakanishi) Scattering for the Gross-Pitaevskii equation, Math. Research Letters 13 (2006), no.2, 273--285. | math/ 0510080 pdf |
| 13 | (with Y. Martel and F. Merle) Stability in H^1 of the sum of K solitary waves for some nonlinear Schrödinger equations, Duke Math. J. 133, no. 3 (2006), 405--466. | |
| 14 | (with S. Gustafson and K. Kang) Schrödinger flow near harmonic maps, Comm. Pure Appl. Math. 60 (2007) no. 4, 463--499. | math/ 0504497 pdf |
| 15 | (with S.-M. Chang, S. Gustafson, and K. Nakanishi) Spectra of linearized operators of NLS solitary waves, SIAM Journal on Mathematical Analysis 39 (2007), no 4. 1070--1111. | math.AP/ 0611483 pdf |
| 16 | (with M.A. Moyers-Gonzalez, I.A. Frigaard and O. Scherzer) Transient effects in oilfield cementing flows: Qualitative behaviour, European Journal of Applied Math. 18 (2007), 477--512. | |
| 17 | (with S. Gustafson and K. Kang) Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations, Commun. Math. Phys. 273 (2007), 161--176. | math.AP/ 0607114 pdf |
| 18 | (with S. Gustafson and K. Nakanishi) Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions, Annales Henri Poincar\'e 8 (2007), 1303--1331. | math.AP/ 0605655 pdf |
| 19 | (with S. Gustafson and K. Kang) Asymptotic stability of harmonic maps under the Schrödinger flow, Duke Math. J. 145, No. 3 (2008), 537-583. | math.AP/ 0609591 pdf |
| 20 |
C.-C. Chen, R. M. Strain, T.-P. Tsai and H.-T. Yau,
Lower bound on the blow-up rate of the axisymmetric Navier-Stokes
equations,
Int. Math. Res. Not., (2008) Vol. 2008 : article ID rnn016, 31 pages.
https://doi.org/10.1093/imrn/rnn016
Errata: (i) There is a typo on page 21: All "a" on page 21 should be replaced by "\beta". There are 5 of them. (ii) The journal put me as the last author probably because I was the corresponding author, although in both the submission and revision files (and also in arxiv), I was the third author according to the alphabetical order. |
math.AP/ 0701796 pdf |
| 21 | M. Guan, S. Gustafson and T.-P. Tsai, Global existence and blow-up for harmonic map heat flow, J. Diff. Equations 246 (2009) 1--20. | |
| 22 | S. Gustafson, K. Nakanishi and T.-P. Tsai, Scattering theory for the Gross-Pitaevskii equation in three dimensions, Communications in Contemporary Mathematics 11, No. 4 (2009) 657-707. | 0803.3208 |
| 23 | S. Gustafson, H. Takaoka and T.-P. Tsai, Stability in $H^{1/2}$ of the sum of $K$ solitons for the Benjamin-Ono equation, Journal of Mathematical Physics 50, 013101 (2009). | 0803.3783 pdf |
| 24 | Chiun-Chuan Chen, Robert M. Strain,T.-P. Tsai, and Horng-Tzer Yau, Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations II, Communications in Partial Differential Equations, Volume 34, Issue 3 March 2009 , pages 203 - 232 . | 0709.4230 pdf |
| 25 | S. Gustafson, K. Nakanishi, T.-P. Tsai, Asymptotic stability, concentration, and oscillation in harmonic map heat-flow, Landau-Lifshitz, and Schrödinger maps on R^2, Comm. Math. Phys. 300, 205-242 (2010) |
0904.0461
pdf
|
| 26 | Hideyuki Miura and T.-P. Tsai, Point singularities of 3D stationary Navier-Stokes flows, Journal of Mathematical Fluid Mechanics, 2012, Volume 14, Number 1, Pages 33-41. |
0810.2004 |
| 27 | K. Nakanishi, T. V. Phan, and T.-P. Tsai, Small solutions of nonlinear Schrödinger equations near first excited states, Journal of Functional Analysis, Volume 263, Issue 3, 1 August 2012, 703-781 |
1008.3581
|
| 28 | K. Kang, H. Miura, and T.-P. Tsai, Asymptotics of small exterior Navier-Stokes flows with non-decaying boundary data, Comm. Partial Differential Equations 37 (2012) no.10 1717-1753. |
1105.0414
|
| 29 | T.-P.
Tsai, Forward discretely self-similar solutions
of the Navier-Stokes equations,
Commun. Math. Phys. 328 (2014) no.1, 29-44.
DOI 10.1007/s00220-014-1984-2
|
1210.2783
|
| 30 | Y. Luo and T.-P. Tsai,
Regularity criteria in weak $L^3$ for 3D incompressible
Navier-Stokes equations,
Funkcialaj Ekvacioj 58 (2015) 387--404.
|
1310.8307
|
| 31 |
D. Chae and T.-P. Tsai,
On discretely self-similar solutions of the Euler equations,
Mathematical Research Letters 21 (2014) 437-447
|
1304.7414 |
| 32 | S. Le Coz, D. Li,
and T.-P. Tsai, Fast-moving finite and infinite trains of solitons for
nonlinear Schrödinger equations,
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145
(2015),
no.6, 1251-1282
DOI:10.1017/S030821051500030X
|
1304.3049 |
| 33 | S. Le Coz and T.-P.
Tsai, Infinite soliton and kink-soliton trains for nonlinear
Schrödinger equations,
Nonlinearity 27 (2014) 2689-2709.
| 1309.7846
|
| 34 | D. Chae and
T.-P. Tsai,
Remark on Luo-Hou's ansatz for a self-similar solution to the 3D Euler equations,
Journal of Nonlinear Science 25 (2015), no.1, 193--202.
DOI 10.1007/s00332-014-9225-6
| 1402.4560 |
| 35 | M. Korobkov and T.-P. Tsai,
Forward self-similar solutions of the Navier-Stokes equations in the
half space,
Analysis & PDE 9(8), (2016), 1811--1827. DOI 10.2140/apde.2016.9.1811
| 1409.2516 |
| 36 |
Liren Lin and T.-P. Tsai, Mixed dimensional infinite soliton trains for nonlinear
Schrödinger equations,
Discrete and Continuous Dynamical Systems - Series A
Volume 37, Issue 1, 2017 Pages 295-336. |
1502.02337
|
| 37 | Z. Bradshaw and T.-P. Tsai,
Forward discretely self-similar solutions of the Navier-Stokes equations II.
Annales Henri Poincare, 18(3), 1095-1119
(2016). doi:10.1007/s00023-016-0519-0
| 1510.07504 |
| 38 | Z. Bradshaw and T.-P. Tsai, Rotationally corrected scaling invariant solutions to the Navier-Stokes equations, Communications in Partial Differential Equations 42 no 7, 2017, 1065-1087 |
1610.05680
|
| 39 | S. Gustafson, S. Le Coz, and T.-P. Tsai, Stability of periodic waves of 1D cubic nonlinear Schrödinger equations, Applied Mathematics Research Express, Volume 2017, Issue 2, 431-487, https://doi.org/10.1093/amrx/abx004 |
1606.04215
|
| 40 | K. Kang, H. Miura, and T.-P. Tsai, Green tensor of the Stokes system and asymptotics of stationary Navier-Stokes flows in the half space, Advances in Mathematics, Volume 323, 7 January 2018, 326-366 https://doi.org/10.1016/j.aim.2017.10.031 |
1606.01854
|
| 41 | Z. Bradshaw and T.-P. Tsai, Discretely self-similar solutions to the Navier-Stokes equations with Besov space data, Archive for Rational Mechanics and Analysis, July 2018, Volume 229, Issue 1, pp 53-77, https://doi.org/10.1007/s00205-017-1213-1 |
1703.03480
|
| 42 | Z. Bradshaw and T.-P. Tsai, Discretely self-similar solutions to the Navier-Stokes equations with data in $L^2_{loc}$ satisfying the local energy inequality, Analysis and PDE 12 (2019), no. 8, 1943-1962. https://doi.org/10.2140/apde.2019.12.1943 |
1801.08060
|
| 43 | K. Kang, H. Miura, and T.-P. Tsai, Short time regularity of Navier-Stokes flows with locally $L^3$ initial data and applications Int. Math. Res. Not., 2020, rnz327 https://doi.org/10.1093/imrn/rnz327 |
1812.10509
|
| 44 | H. Kwon and T.-P. Tsai, Global Navier-Stokes flows for non-decaying initial data with slowly decaying oscillation, Commun. Math. Phys. 375, 1665-1715 (2020). https://doi.org/10.1007/s00220-020-03695-3 |
1811.03249
|
| 45 | H. Kim and T.-P. Tsai, Existence, uniqueness, and regularity results for elliptic equations with drift terms in critical weak spaces, SIAM J. Math. Anal. 52 (2020), no. 2, 1146-1191. https://doi.org/10.1137/19M1282969 |
1811.03201
|
| 46 | Z. Bradshaw and T.-P. Tsai, Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations, Communications in Partial Differential Equations 45 (2020), no. 9, 1168-1201, https://doi.org/10.1080/03605302.2020.1761386 |
1907.00256
|
| 47 | Z. Bradshaw, I. Kukavika, and T.-P. Tsai, Existence of global weak solutions to the Navier-Stokes equations in weighted spaces, Indiana Univ. Math. J. 71 (2022), no. 1, 191-212 |
1910.06929
|
| 48 | T.-P. Tsai, Liouville type theorems for stationary Navier-Stokes equations, SN Partial Differ. Equ. Appl. 2, 10 (2021). https://doi.org/10.1007/s42985-020-00056-6 |
2005.09691
|
| 49 | Z. Bradshaw and T.-P. Tsai, Local energy solutions to the Navier-Stokes equations in Wiener amalgam spaces, SIAM J. Math. Anal. 53 (2021) no. 2, 1993-2026. |
2008.09204
|
| 50 | H. Kwon and T.-P. Tsai, On bifurcation of self-similar solutions of the stationary Navier-Stokes equations, Commun Math Sci. 19 (2021) no. 6, 1703-1733. https://dx.doi.org/10.4310/CMS.2021.v19.n6.a11 |
2011.02800
|
| 51 | F. Liu, T.-P. Tsai, and I. Zwiers, Existence and stability of standing waves for one dimensional NLS with triple power nonlinearities, Nonlinear Analysis 211 (2021), 112409 |
2102.01246
|
| 52 | K. Kang, H. Miura, and T.-P. Tsai, An $\epsilon$-regularity criterion and estimates of the regular set for Navier-Stokes flows in terms of initial data, Pure and Applied Analysis 3 (2021) 567-594 |
2006.13145
|
| 53 | Z. Bradshaw and T.-P. Tsai, On the local pressure expansion for the Navier-Stokes equations, J. Math. Fluid Mech. 24, 3 (2022). https://doi.org/10.1007/s00021-021-00637-4 |
2001.11526
|
| 54 | K. Kang, H. Miura, and T.-P. Tsai, Local regularity conditions on initial data for local energy solutions of the Navier-Stokes equations, Partial Differ. Equ. Appl. 3, 5 (2022). https://doi.org/10.1007/s42985-021-00127-2 |
2106.03980
|
| 55 | P. Kfoury, S. Le Coz, and T.-P. Tsai, Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schr\"odinger equation, C. R. Math. Acad. Sci. Paris 360 (2022), 867-892. |
2112.06529
|
| 56 | H. Chen, T.-P. Tsai and T. Zhang, Remarks on local regularity of axisymmetric solutions to the 3D Navier-Stokes equations, Communications in Partial Differential Equations, 47:8, 1680-1699 (2022) https://doi.org/10.1080/03605302.2022.2070854 . Erratum to: Remarks on local regularity of axisymmetric solutions to the 3D Navier-Stokes equations, https://doi.org/10.1080/03605302.2023.2215296 |
2201.01766
|
| 57 | K. Kang, B. Lai, C.-C. Lai, and T.-P. Tsai, The Green tensor of the nonstationary Stokes system in the half space, Communications in Mathematical Physics 399, 1291-1372 (2023) https://doi.org/10.1007/s00220-022-04623-3 |
2011.00134
|
| 58 | K. Kang, B. Lai, C.-C. Lai, and T.-P. Tsai, Finite energy Navier-Stokes flows with unbounded gradients induced by localized flux in the half-space, Transaction of AMS 375 (2022) No. 9, 6701-6746. |
2107.00810
|
| 59 | Z. Bradshaw, C.-C. Lai, and T.-P. Tsai, Mild solutions and spacetime integral bounds for Stokes and Navier-Stokes flows in Wiener amalgam spaces, Mathematische Annalen (2023) |
2207.04298
|
| 60 |
Hui Chen, Su Liang,
and Tai-Peng Tsai,
Gradient estimates for the non-stationary Stokes system with the Navier boundary condition,
Communications on Pure and Applied Analysis, 2023, Doi: 10.3934/cpaa.2023120,
special issue for Sverak's 65th birthday
|
2306.16480
|
| B. PREPRINTS | ||
|
V. Combet, T.-P. Tsai, and I. Zwiers,
Local dynamics near unstable branches of NLS solitons, arXiv 2012
|
1207.0175
| |
|
Stephen Gustafson,
Evan Miller,
and Tai-Peng Tsai,
Growth rates for anti-parallel vortex tube Euler flows in three and higher dimensions
|
2303.12043 | |
|
Zachary Bradshaw, Misha Chernobai and Tai-Peng Tsai,
Global Navier-Stokes flows in intermediate spaces
|
2310.15142 | |
|
Theo Morrison and Tai-Peng Tsai,
On standing waves of 1D nonlinear Schr\"odinger equation with triple power nonlinearity
|
2312.03693
| |
|
Hyunseok Kim, Tuoc Phan, and Tai-Peng Tsai.
On linear elliptic equations with drift terms in critical weak spaces
|
2312.11215
| |
| C. BOOKS AND CHAPTERS | ||
| c1 | H. Jia, V. Sverak, and T.-P. Tsai,
(2018) Self-Similar Solutions to the Nonstationary Navier-Stokes Equations. In: Giga Y., Novotny A. (eds)
Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham.
https://doi.org/10.1007/978-3-319-13344-7_9
| |
| c2 | T.-P. Tsai,
Lectures on Navier-Stokes
Equations.
Graduate Studies in Mathematics, 192. American Mathematical Society,
Providence, RI, 2018.
http://dx.doi.org/10.1090/gsm/192
| |
| D. PROCEEDINGS AND OTHERS | ||
| d1 | T.-P. Tsai, (Doctoral Dissertation) On problems arising in the regularity theory for the Navier-Stokes equations. University of Minnesota, 1998. | |
| d2 | J. Froehlich, H.-T. Yau and T.-P. Tsai, On a classical limit of quantum theory and the non-linear Hartree equation, GAFA 2000 (Tel Aviv, 1999). Geom. Funct. Anal. 2000, Special Volume, Part I, 57--78. Also in Conférence Moshé Flato 1999, Vol. I (Dijon), 189--207, Math. Phys. Stud., 21, Kluwer Acad. Publ., Dordrecht, 2000. | |
| d3 | T.-P. Tsai, Soliton Dynamics of Nonlinear Schrödinger Equations. In Second International Congress of Chinese Mathematicians, volume 4 of New Stud. Adv. Math., pages 547-554. Int. Press, Somerville, MA, 2004. | |
| d4 | M. Guan, S. Gustafson, K. Kang and T.-P. Tsai, Global questions for map evolution equations. Singularities in PDE and the calculus of variations, 61--74, CRM Proc. Lecture Notes, 44, Amer. Math. Soc., Providence, RI, 2008. | |
| d5 | S. Le Coz and T.-P. Tsai,
Finite and infinite soliton and kink-soliton
trains of nonlinear
Schrödinger equations,
Proceedings of the Sixth International Congress of Chinese Mathematicians. Vol.
I, 4356, Adv. Lect. Math. (ALM), 36, Int. Press, Somerville, MA, 2017.
| 1409.8379 |
| d6 |
Jing Yu, Mu-Tao Wang, Tai-Peng Tsai, Ming-Lun Hsieh, and Jeng-Daw Yu,
Fu Sinian Awards,
Notices of the International Congress of Chinese Mathematicians
Volume 3 (2015)
Number 1, pp. 94-96
|
|
| d7 | Z. Bradshaw and T.-P. Tsai, Self-similar solutions to the Navier-Stokes equations: a survey of recent results, in Nonlinear Analysis in Geometry and Applied Mathematics, Part 2, 159-181, Harv. Univ. Cent. Math. Sci. Appl. Ser. Math., 2, Int. Press, Somerville, MA, 2018. |
1802.00038
|
Department of Mathematics | University of British Columbia orcid updated: 1-46, 48, c1-c2, d1-d4 |