Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4

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MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS (2013, background): “ is defocusing and analytic (podd integer). In this case, global smooth solutions disperse and in many cases even scatter to a linear state (possibly after modulation by a real phase when d= 1, p= 3) [28, 30, 33, 35, 36, 55, 69, 70, 76, 81, 89, 91]. In contrast, much less is known for compact domain”
The cubic nonlinear Schr\"odinger equation in two dimensions with radial data (2007, methodology): “The argument used to deduce Corollary 1.12 works in any dimension and without the assumption of spherical symmetry; it just relies on an affirmative answer to Conjecture 1.8.”
The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions (2005, background): “T. Tao, [32], settled the problem for arbitrary dimensions (with an improvement in the final bound due to a simplification of the argument), but again only for radially symmetric data.”