Tai-Peng Tsai: Publications


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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 Schroedinger 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 Schroedinger 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 Schroedinger 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 Schr\"odinger 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 Schroedinger 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 Schr\"odinger 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 Schr\"odinger equations, Duke Math. J. 133, no. 3 (2006), 405--466. pdf
14(with S. Gustafson and K. Kang) Schr\"odinger 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 Schr\"odinger flow, Duke Math. J. 145, No. 3 (2008), 537-583. arxiv pdf
20 (with Chiun-Chuan Chen, Robert M. Strain, Horng-Tzer 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.
Erratum: There is a typo on page 21: All "a" on page 21 should be replaced by \beta. There are 5 of them. 		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
23S. 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, Horng-Tzer Yau, and T.-P. Tsai, 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 Schroedinger maps on R^2, Comm. Math. Phys. 300, 205-242 (2010) arxiv pdf
26Hideyuki 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
27K. Nakanishi, T. V. Phan, and T.-P. Tsai, Small solutions of nonlinear Schr\"odinger equations near first excited states, Journal of Functional Analysis, Volume 263, Issue 3, 1 August 2012, 703-781 arxiv
28K. 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
B. SUBMITTED
29 V. Combet, T.-P. Tsai, and I. Zwiers, Local dynamics near unstable branches of NLS solitons, submitted.
 arxiv
30T.-P. Tsai, Forward discrete self-similar solutions of the Navier-Stokes equations, submitted.
 arxiv
31 S. Le Coz, D. Li, and T.-P. Tsai, Fast-moving finite and infinite trains of solitons for nonlinear Schr\"odinger equations, submitted.
 arxiv
C. PROCEEDINGS AND OTHERS
c1 (Doctoral Dissertation) On problems arising in the regularity theory for the Navier-Stokes equations. University of Minnesota, 1998. 
c2(with J. Froehlich and H.-T. Yau) 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.  
c3Soliton Dynamics of Nonlinear Schr\"odinger Equations, to appear in the proceedings of ICCM II (Taipei 2001).  
c4 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


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