|   [1] Adams R A. Sobolev Space. New York, London: Academic Press, 1975 
 
[2] Bourgain J. Global well-posedness of defocusing critical nonlinear Schr¨odinger equation in the radial case. J Amer Math Soc, 1999, 12: 145–171 
 
[3] Cao D, Guo Q. Divergent solutions to the 5D Hartree equations. Colloq Math, 2011, 125: 255–287 
 
[4] Cao D, Han P. Inhomogeneous critical nonlinear Schr¨odinger equations with a harmonic potential. J Math Phys, 2010, 51: 043505 
 
[5] Cazenave T, Haraux A. An Introduction to Semilinear Evolution Equations. New York: Oxford University Press, 1998 
 
[6] Cazenave T, Weissler F B. The Cauchy problem for the critical nonlinear Schr¨odinger equation in Hs. Nonlinear Anal, 1990, 14: 807–836 
 
[7] Cazenave T,Weissler F B. Some remarks on the nonlinear Schr¨odinger equation in the critical case//Lecture 
Notes in Math, 1394. Berlin: Springer, 1989: 18–29 
 
[8] Colliander J, Keel M, Staffilani G, Takaoke H, Tao T. Global well-posedness and scattering for the energycritical 
nonlinear Schr¨odinger equation in R3. Ann Math, 2008, 167: 767–865 
 
[9] Gan Z, Guo B. Blow-up phenomena of the vector nonlinear Schr¨odinger equations with magnetic fields. Sci China Math, 2011, 54: 2111–2122 
 
[10] Gan Z, Guo B, Zhang J. Blowup and global existence of the nonlinear Schr¨odinger equations with multiple potentials. Commun Pure Appl Anal, 2009, 8: 1303–1312 
 
[11] Gan Z, Zhang J. Blow-up, global existence and standing waves for the magnetic nonlinear Schr¨odinger equations. Discrete Contin Dyn Syst, 2012, 32: 827–846 
 
[12] Gan Z, Zhang J. Sharp criterions of global existence and collapse for coupled nonlinear Schr¨odinger equations. 
J Partial Differ Equ, 2004, 17: 207–220 
 
[13] Ginibre J, Velo G. On a class of nonlinear Schr¨odinger equations. J Funct Anal, 1979, 32: 1–71 
 
[14] Glassey R T. On the blowup of nonlinear Schr¨odinger equations. J Math Phys, 1977, 18: 1794–1797 
 
[15] Grillakis M G. On nonlinear Schr¨odinger equations. Comm Partial Differ Equ, 2000, 25: 1827–1844 
 
[16] Han P. Global well-posedness and scattering for the focusing nonlinear Schr¨odinger equation in the nonradial 
case. Opuscula Math, 2012, 32: 487–504 
 
[17] Liu Z, Han P. On a class of critical heat equations with an inverse square potential. Differential Integral Equations, 2007, 20: 27–50 
 
[18] Kenig C E, Merle F. Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear 
Schr¨odinger equation in the radial case. Invent Math, 2006, 166: 645–675 
 
[19] Killip R, Visan M. The focusing energy-critical nonlinear Schr¨odinger equation in dimensions five and higher. Amer J Math, 2010, 132: 361–424 
 
[20] Merle F. Nonexistence of minimal blow-up solutions of equation iut = −Δu−k(x)|u|4/N u in RN. Ann Inst Henri 
Poincar´e Physique Th´erique, 1996, 64: 33–85 
 
[21] Ogawa T, Tsutsumi Y. Blow-up of H1-solution for the nonlinear Schr¨odinger equation. J Differ Equ, 1991, 92: 317–330 
 
[22] Ogawa T, Tsutsumi Y. Blow-up of H1-solution for the nonlinear Schr¨odinger equation with critical power 
nonlinearity. Proc Amer Math Soc, 1991, 111: 487–496 
 
[23] Ryckman E, Visan M. Global well-posedness and scattering for the defocusing energy-critical nonlinear Schr¨odinger equation in R1+4. Amer J Math, 2007, 129: 1–60 
 
[24] Strauss W A. Existence of solitary waves in higher dimensions. Comm Math Phys, 1977, 55: 149–162 
 
[25] Talenti G. Best constant in Sobolev inequality. Ann Mat Pura Appl, 1976, 110: 353–372 
 
[26] Tao T. Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schr¨odinger 
equation for radial data. New York J Math, 2005, 11: 57–80 
 
[27] Visan M. The defocusing energy-critical nonlinear Schr¨odinger equation in higher dimensions. Duke Math 
J, 2007, 138: 281–374 
 
[28] Weinstein M I. Nonlinear Schr¨odinger equations and sharp interpolation estimates. Comm Math Phys, 1983, 87: 567–576  |