Sharp conditions of global existence for nonlinear Schrödinger and Klein--Gordon equations

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On the blow-up solutions for the nonlinear Schrödinger equation with combined power-type nonlinearities (2018, background): “Weinstein [21], Zhang [23] obtained the sharp conditions of global existence for L2-critical and L2-supercritical nonlinearities.”
Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case (2006, result): “[30] Zhang, Jian Sharp conditions of global existence for nonlinear Schrödinger and Klein-Gordon equations.”
Sharp threshold of blow-up and scattering for the fractional Hartree equation (2017, methodology): “Similar to studies on the classical semi-linear Schrödinger equation (see[5, 33, 34]), we attempt to use the variational method to find a sharp threshold of blow-up and global existence of the solutions to (1.”
Sharp Threshold for Blowup and Global Existence in Nonlinear Schrödinger Equations Under a Harmonic Potential (2005, background): “Especially the sharp thresholds for blowup and global existence are pursued strongly (see Dalfovo et al., 1999; Kagan et al., 1996, 1998; Sackett et al., 1999; Sulem and Sulem, 1999; Ueda and Leggett, 1998; Wadati and Tsurumi, 1998; Zhang, 1994, 2002).”