# Tai-Peng Tsai: Publications

orcid.org ID: 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 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, 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 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). arxiv 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 . arxiv 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) arxiv 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. 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, 703-781 arxiv 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. arxiv 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 arxiv 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. arxiv 31 D. Chae and T.-P. Tsai, On discretely self-similar solutions of the Euler equations, Mathematical Research Letters 21 (2014) 437-447 arxiv 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 arxiv pdf 33 S. Le Coz and T.-P. Tsai, Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations, Nonlinearity 27 (2014) 2689-2709. arxiv 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 arxiv 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 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 295-336. arxiv 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 arxiv 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 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, 431-487, 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 Navier-Stokes flows in the half space, Advances in Mathematics, Volume 323, 7 January 2018, 326-366 arxiv 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 arxiv 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, to appear arxiv 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. to appear arxiv B. PREPRINTS 44 V. Combet, T.-P. Tsai, and I. Zwiers, Local dynamics near unstable branches of NLS solitons, 2012 arxiv 45 H. Kim and T.-P. Tsai, Existence, uniqueness, and regularity results for elliptic equations with drift terms in critical weak spaces arxiv 46 H. Kwon and T.-P. Tsai, Global Navier-Stokes flows for non-decaying initial data with slowly decaying oscillation arxiv 47 Z. Bradshaw and T.-P. Tsai, Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations arxiv 48 Z. Bradshaw, I. Kukavika, and T.-P. Tsai, Existence of global weak solutions to the Navier-Stokes equations in weighted spaces 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 Navier-Stokes 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 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 c7 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