
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. 
pdf

3  (with J. Froehlich and H.T. Yau) On
the pointparticle (Newtonian) limit of the nonlinear Hartree equation,
Comm. Math. Phys. 225 (2002), 223274. 
pdf 
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. 
pdf 
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.
 pdf 
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,
doi: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).  arxiv 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 .

arxiv
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)

arxiv
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.

arxiv

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

arxiv

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.

arxiv

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

arxiv

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

arxiv

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

arxiv

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

arxiv
pdf

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

arxiv

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
 arxiv

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
 arxiv

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.

arxiv

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
 arxiv

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

arxiv

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

arxiv

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

arxiv

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

arxiv

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.

arxiv

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. rnz327 https://doi.org/10.1093/imrn/rnz327

arxiv

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

arxiv

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.

arxiv

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,
https://doi.org/10.1080/03605302.2020.1761386

arxiv

47  Z. Bradshaw, I. Kukavika, and T.P.
Tsai,
Existence of global weak solutions to the NavierStokes equations in weighted spaces,
Indiana University Mathematics Journal, to appear.

arxiv

B. PREPRINTS

48 
V. Combet, T.P. Tsai, and I. Zwiers,
Local dynamics near unstable branches of NLS solitons, arXiv 2012

arxiv

49  Z. Bradshaw and T.P.
Tsai,
On the local pressure expansion for the NavierStokes equations

arxiv

50 
T.P. Tsai,
Liouville type theorems for stationary NavierStokes equations

arxiv

51  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

arxiv

C. BOOKS AND CHAPTERS

c1  H. Jia, V. Sverak, and T.P. Tsai,
Self similar solutions to the nonstationary Navier Stokes
equations,
a chapter in Handbook of Mathematical Analysis in Mechanics of Viscous
Fluids, edited by Y. Giga and A. Novotny, Springer


c2  T.P. Tsai,
Lectures on NavierStokes
Equations.
Graduate Studies in Mathematics, 192. American Mathematical Society,
Providence, RI, 2018.


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.

pdf

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


c7  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

 