[1] I. Bejenaru, A. Ionescu, C. Kenig and D. Tataru: Global Schr¨odinger maps in dimensions d ≥ 2: Small data in the critical Sobolev spaces, Ann. Math. (2) 173 (2011), 1443-1506.
[2] L. Caffarelli, R. Kohn and L. Nirenberg: First order interpolation inequalities with weights, Composito Math. 53 (1984), 259–275.
[3] N.H. Chang, J. Shatah and K. Uhlenbeck: Schr¨odinger maps, Comm. Pure. Appl. Math. 53 (2000), 590– 602.
[4] M. Daniel, K. Porsezian and M. Lakshmanan: On the integrability of the inhomogeneous spherically symmetric Heisenberg ferromagnet in arbitrary dimensions, J. Math. Phys. 35 (1994), 6498–6510.
[5] R.T. Glassey: On the blowing up of solutions to the Cauchy problem for nonlinear Schr¨odinger equations, J. Math. Phys. 18 (1976), 1794–1797.
[6] W. Ichinose: The Cauchy problem for Schr¨odinger type equations with variable coefficients, Osaka J. Math. 24 (1987), 853–886.
[7] C. Kenig, G. Ponce and L. Vega: On the Cauchy problem for linear Schr¨odinger systems with variable coefficient lower order terms; in Harmonic Analysis and Number Theory (Montreal PQ, 1996), CMS Conference Proceedings 21, Amer. Math. Soc., Providence, RI, 1997, 205–227.
[8] H. McGahagan: An approximation scheme for Schr¨odinger maps, Comm. Partial Differential Equations 32 (2007), 375–400.
[9] F. Merle, P. Raphael and I. Rodnianski: ¨ Blow-up dynamics for smooth data equivariant solutions to the critical Schr¨odinger map problem, Invent. Math. 193 (2013), 249–365.
[10] P.Y.H. Pang, H.Y. Tang and Y.D. Wang: Blow-up solutions of inhomogeneous nonlinear Schr¨odinger Equations, Calc. Var. Partial Differential Equations 26 (2006), 137–169.
[11] G. Perelman: Blow up dynamics for equivariant critical Schr¨odinger maps, Comm. Math. Phys. 330 (2014), 69–105.
[12] K. Porsezian and M. Lakshmanan: On the dynamics of the radially symmetric Heisenberg ferromagnetic spin system, J. Math. Phys. 32 (1991), 2923–2928.
[13] G. Staffilani and D. Tataru: Strichartz estimates for a Schr¨odinger operator with nonsmooth coefficients, Comm. Partial Differential Equations 27 (2002), 1337–1372.
[14] C. Sulem, P.L. Sulem and C. Bardos: On the continuous limit for a system of classical spins, Comm. Math. Phys. 107 (1986), 431–454.
[15] J. Zhai and B. Zheng: On the local well-posedness for the nonlinear Schr¨odinger equation with spatial variable coefficient, J. Math. Anal. Appl. 445 (2017), 81–96.
[16] J. Zhai and B. Zheng: Global existence and blow-up solutions of the radial Schr¨odinger maps, Commun. Contemp. Math. 23 (2021), 2050009, 22pp.
[17] B. Zheng: On the well-posedness for the nonlinear radial Schr¨odinger equation with spatial variable coefficients, Nonlinear Anal. 182 (2019), 1–19.