orcid https://orcid.org/0000000290081136
A. REFEREEED JOURNAL PAPERS  
1  On Leray's selfsimilar solutions of the NavierStokes equations satisfying local energy estimates, Archive for Rational Mechanics and Analysis, 143; (1998) 2951.  pdf err 
2  (with V. Sverak) On the spatial decay of 3D steadystate NavierStokes flows. Comm. Partial Differential Equations, 25 (2000), no. 11&12, 21072117.  
3  (with J. Froehlich and H.T. Yau) On the pointparticle (Newtonian) limit of the nonlinear Hartree equation, Comm. Math. Phys. 225 (2002), 223274.  
4  (with H.T. Yau) Asymptotic dynamics of nonlinear Schrödinger equations: resonance dominated and dispersion dominated solutions, Comm. Pure Appl. Math. 55 (2002) 01530216.  arxiv pdf 
5  (with H.T. Yau) Relaxation of excited states in nonlinear Schrödinger equations, Int. Math. Res. Not. 2002 (2002), no. 31, 16291673.  arxiv pdf 
6  (with H.T. Yau) Stable directions for excited states of nonlinear Schrödinger equations, Comm. Partial Differential Equations 27 (2002), no. 11&12, 23632402.  arxiv 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, 107139.  arxiv 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, 347373.  arxiv pdf 
9  Asymptotic dynamics of nonlinear Schrödinger equations with many bound states, J. Diff. Equations 192 (2003), no 1, 225282.  arxiv private 
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, 35593584.  arxiv pdf 
11  (with S. Gustafson and K. Kang) Regularity criteria for suitable weak solutions to the NavierStokes equations near the boundary, J. Diff. Equations 226 (2006) 594618.  arxiv private 
12  (with S. Gustafson and K. Nakanishi) Scattering for the GrossPitaevskii equation, Math. Research Letters 13 (2006), no.2, 273285.  arxiv 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), 405466.  
14  (with S. Gustafson and K. Kang) Schrödinger flow near harmonic maps, Comm. Pure Appl. Math. 60 (2007) no. 4, 463499.  arxiv 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. 10701111.  arxiv pdf 
16  (with M.A. MoyersGonzalez, I.A. Frigaard and O. Scherzer) Transient effects in oilfield cementing flows: Qualitative behaviour, European Journal of Applied Math. 18 (2007), 477512.  
17  (with S. Gustafson and K. Kang) Interior regularity criteria for suitable weak solutions of the NavierStokes equations, Commun. Math. Phys. 273 (2007), 161176.  arxiv pdf 
18  (with S. Gustafson and K. Nakanishi) Global dispersive solutions for the GrossPitaevskii equation in two and three dimensions, Annales Henri Poincar\'e 8 (2007), 13031331.  arxiv pdf 
19  (with S. Gustafson and K. Kang) Asymptotic stability of harmonic maps under the Schrödinger flow, Duke Math. J. 145, No. 3 (2008), 537583.  arxiv pdf 
20 
C.C. Chen, R. M. Strain, T.P. Tsai and H.T. Yau,
Lower bound on the blowup rate of the axisymmetric NavierStokes
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. 
arxiv pdf 
21  M. Guan, S. Gustafson and T.P. Tsai, Global existence and blowup for harmonic map heat flow, J. Diff. Equations 246 (2009) 120.  private 
22  S. Gustafson, K. Nakanishi and T.P. Tsai, Scattering theory for the GrossPitaevskii equation in three dimensions, Communications in Contemporary Mathematics 11, No. 4 (2009) 657707.  arxiv private 
23  S. Gustafson, H. Takaoka and T.P. Tsai, Stability in $H^{1/2}$ of the sum of $K$ solitons for the BenjaminOno equation, Journal of Mathematical Physics 50, 013101 (2009).  0803.3783 pdf 
24  ChiunChuan Chen, Robert M. Strain,T.P. Tsai, and HorngTzer Yau, Lower bound on the blowup rate of the axisymmetric NavierStokes 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 heatflow, LandauLifshitz, and Schrödinger maps on R^2, Comm. Math. Phys. 300, 205242 (2010) 
0904.0461
pdf

26  Hideyuki Miura and T.P. Tsai, Point singularities of 3D stationary NavierStokes flows, Journal of Mathematical Fluid Mechanics, 2012, Volume 14, Number 1, Pages 3341. 
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, 703781 
1008.3581

28  K. Kang, H. Miura, and T.P. Tsai, Asymptotics of small exterior NavierStokes flows with nondecaying boundary data, Comm. Partial Differential Equations 37 (2012) no.10 17171753. 
1105.0414

29  T.P.
Tsai, Forward discretely selfsimilar solutions
of the NavierStokes equations,
Commun. Math. Phys. 328 (2014) no.1, 2944.
DOI 10.1007/s0022001419842

1210.2783

30  Y. Luo and T.P. Tsai,
Regularity criteria in weak $L^3$ for 3D incompressible
NavierStokes equations,
Funkcialaj Ekvacioj 58 (2015) 387404.

1310.8307

31 
D. Chae and T.P. Tsai,
On discretely selfsimilar solutions of the Euler equations,
Mathematical Research Letters 21 (2014) 437447

1304.7414 
32  S. Le Coz, D. Li,
and T.P. Tsai, Fastmoving finite and infinite trains of solitons for
nonlinear Schrödinger equations,
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145
(2015),
no.6, 12511282
DOI:10.1017/S030821051500030X

1304.3049 
33  S. Le Coz and T.P.
Tsai, Infinite soliton and kinksoliton trains for nonlinear
Schrödinger equations,
Nonlinearity 27 (2014) 26892709.
 1309.7846

34  D. Chae and
T.P. Tsai,
Remark on LuoHou's ansatz for a selfsimilar solution to the 3D Euler equations,
Journal of Nonlinear Science 25 (2015), no.1, 193202.
DOI 10.1007/s0033201492256
 1402.4560 
35  M. Korobkov and T.P. Tsai,
Forward selfsimilar solutions of the NavierStokes equations in the
half space,
Analysis & PDE 9(8), (2016), 18111827. 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 295336. 
1502.02337

37  Z. Bradshaw and T.P. Tsai,
Forward discretely selfsimilar solutions of the NavierStokes equations II.
Annales Henri Poincare, 18(3), 10951119
(2016). doi:10.1007/s0002301605190
 1510.07504 
38  Z. Bradshaw and T.P. Tsai, Rotationally corrected scaling invariant solutions to the NavierStokes equations, Communications in Partial Differential Equations 42 no 7, 2017, 10651087 
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, 431487, 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 NavierStokes flows in the half space, Advances in Mathematics, Volume 323, 7 January 2018, 326366 https://doi.org/10.1016/j.aim.2017.10.031 
1606.01854

41  Z. Bradshaw and T.P. Tsai, Discretely selfsimilar solutions to the NavierStokes equations with Besov space data, Archive for Rational Mechanics and Analysis, July 2018, Volume 229, Issue 1, pp 5377, https://doi.org/10.1007/s0020501712131 
1703.03480

42  Z. Bradshaw and T.P. Tsai, Discretely selfsimilar solutions to the NavierStokes equations with data in $L^2_{loc}$ satisfying the local energy inequality, Analysis and PDE 12 (2019), no. 8, 19431962. https://doi.org/10.2140/apde.2019.12.1943 
1801.08060

43  K. Kang, H. Miura, and T.P. Tsai, Short time regularity of NavierStokes 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 NavierStokes flows for nondecaying initial data with slowly decaying oscillation, Commun. Math. Phys. 375, 16651715 (2020). https://doi.org/10.1007/s00220020036953 
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, 11461191. 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 NavierStokes equations, Communications in Partial Differential Equations 45 (2020), no. 9, 11681201, 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 NavierStokes equations in weighted spaces, Indiana Univ. Math. J. 71 (2022), no. 1, 191212 
1910.06929

48  T.P. Tsai, Liouville type theorems for stationary NavierStokes equations, SN Partial Differ. Equ. Appl. 2, 10 (2021). https://doi.org/10.1007/s42985020000566 
2005.09691

49  Z. Bradshaw and T.P. Tsai, Local energy solutions to the NavierStokes equations in Wiener amalgam spaces, SIAM J. Math. Anal. 53 (2021) no. 2, 19932026. 
2008.09204

50  H. Kwon and T.P. Tsai, On bifurcation of selfsimilar solutions of the stationary NavierStokes equations, Commun Math Sci. 19 (2021) no. 6, 17031733. 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 NavierStokes flows in terms of initial data, Pure and Applied Analysis 3 (2021) 567594 
2006.13145

53  Z. Bradshaw and T.P. Tsai, On the local pressure expansion for the NavierStokes equations, J. Math. Fluid Mech. 24, 3 (2022). https://doi.org/10.1007/s00021021006374 
2001.11526

54  K. Kang, H. Miura, and T.P. Tsai, Local regularity conditions on initial data for local energy solutions of the NavierStokes equations, Partial Differ. Equ. Appl. 3, 5 (2022). https://doi.org/10.1007/s42985021001272 
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), 867892. 
2112.06529

56  H. Chen, T.P. Tsai and T. Zhang, Remarks on local regularity of axisymmetric solutions to the 3D NavierStokes equations, Communications in Partial Differential Equations, 47:8, 16801699 https://doi.org/10.1080/03605302.2022.2070854 
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 (2023) https://doi.org/10.1007/s00220022046233 
2011.00134

58  K. Kang, B. Lai, C.C. Lai, and T.P. Tsai, Finite energy NavierStokes flows with unbounded gradients induced by localized flux in the halfspace, Transaction of AMS 375 (2022) No. 9, 67016746. 
2107.00810

59  Z. Bradshaw, C.C. Lai, and T.P. Tsai, Mild solutions and spacetime integral bounds for Stokes and NavierStokes flows in Wiener amalgam spaces, Mathematische Annalen (2023) 
2207.04298

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 TaiPeng Tsai,
Growth rates for antiparallel vortex tube Euler flows in three and higher dimensions

2303.12043  
C. BOOKS AND CHAPTERS  
c1  H. Jia, V. Sverak, and T.P. Tsai,
(2018) SelfSimilar Solutions to the Nonstationary NavierStokes Equations. In: Giga Y., Novotny A. (eds)
Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham.
https://doi.org/10.1007/9783319133447_9
 
c2  T.P. Tsai,
Lectures on NavierStokes
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 NavierStokes equations. University of Minnesota, 1998.  
d2  J. Froehlich, H.T. Yau and T.P. Tsai, On a classical limit of quantum theory and the nonlinear Hartree equation, GAFA 2000 (Tel Aviv, 1999). Geom. Funct. Anal. 2000, Special Volume, Part I, 5778. Also in Conférence Moshé Flato 1999, Vol. I (Dijon), 189207, 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 547554. 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, 6174, CRM Proc. Lecture Notes, 44, Amer. Math. Soc., Providence, RI, 2008.  
d5  S. Le Coz and T.P. Tsai,
Finite and infinite soliton and kinksoliton
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.

arxiv 
d6 
Jing Yu, MuTao Wang, TaiPeng Tsai, MingLun Hsieh, and JengDaw Yu,
Fu Sinian Awards,
Notices of the International Congress of Chinese Mathematicians
Volume 3 (2015)
Number 1, pp. 9496


d7  Z. Bradshaw and T.P. Tsai, Selfsimilar solutions to the NavierStokes equations: a survey of recent results, in Nonlinear Analysis in Geometry and Applied Mathematics, Part 2, 159181, Harv. Univ. Cent. Math. Sci. Appl. Ser. Math., 2, Int. Press, Somerville, MA, 2018. 
arxiv
