# Tai-Peng Tsai: Publications

 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 err 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. pdf 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. pdf 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. arxiv pdf 5 (with H.-T. Yau) Relaxation of excited states in nonlinear Schrödinger equations, Int. Math. Res. Not. 2002 (2002), no. 31, 1629--1673. 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, 2363--2402. 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, 107--139. 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, 347--373. arxiv pdf 9 Asymptotic dynamics of nonlinear Schrödinger equations with many bound states, J. Diff. Equations 192 (2003), no 1, 225-282. 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, 3559--3584. arxiv 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. arxiv private 12 (with S. Gustafson and K. Nakanishi) Scattering for the Gross-Pitaevskii equation, Math. Research Letters 13 (2006), no.2, 273--285. 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), 405--466. pdf 14 (with S. Gustafson and K. Kang) Schrödinger flow near harmonic maps, Comm. Pure Appl. Math. 60 (2007) no. 4, 463--499. 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. 1070--1111. arxiv 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. pdf 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. arxiv 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. 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), 537-583. arxiv 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. arxiv 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. private 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. arxiv private 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 pdf 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 University Mathematics Journal, to appear. 1910.06929 48 T.-P. Tsai, Liouville type theorems for stationary Navier-Stokes equations, SN Partial Differential Equations and Applications (2021)2:10, 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., to appear. 2008.09204 50 H. Kwon and T.-P. Tsai, On bifurcation of self-similar solutions of the stationary Navier-Stokes equations, Commun Math Sci., to appear. 2011.02800 B. PREPRINTS 51 V. Combet, T.-P. Tsai, and I. Zwiers, Local dynamics near unstable branches of NLS solitons, arXiv 2012 1207.0175 52 Z. Bradshaw and T.-P. Tsai, On the local pressure expansion for the Navier-Stokes equations 2001.11526 53 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 2006.13145 54 K. Kang, B. Lai, C.-C. Lai, and T.-P. Tsai, The Green tensor of the nonstationary Stokes system in the half space 2011.00134 55 F. Liu, T.-P. Tsai, and I. Zwiers, Existence and stability of standing waves for one dimensional NLS with triple power nonlinearities 2102.01246 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. pdf 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. arxiv 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. arxiv

Department of Mathematics | University of British Columbia
orcid updated: 1-46, 48, c1-c2, d1-d4 |