article published yes Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca In this short note, we present a new proof of the global well-posedness and scattering result for the defocusing energy-critical nonlinear Schrödinger equation (NLS) in four space dimensions obtained previously by Ryckman and Visan [“Global well-posedness and scattering for the defocusing energycritical nonlinear Schrödinger equation in R^1+4⁠.” American Journal of Mathematics 129 (2007): 1–60. MR2288737]. The argument is inspired by the recent work of Dodson [“Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d≥3.” (2009): preprint arXiv:0912.2467.] on the mass-critical NLS. Oxford University Press2012 eng 1073-7928 1687-0247 1011.152610.1093/imrn/rnr051 201251037-1067 yes M. Vişan, “Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions,” <i>International Mathematics Research Notices</i>, vol. 2012, no. 5. Oxford University Press, pp. 1037–1067, 2012. Vişan M. Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions. <i>International Mathematics Research Notices</i>. 2012;2012(5):1037-1067. doi:<a href="https://doi.org/10.1093/imrn/rnr051">10.1093/imrn/rnr051</a> Vişan, M. (2012). Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnr051">https://doi.org/10.1093/imrn/rnr051</a> M. Vişan, International Mathematics Research Notices 2012 (2012) 1037–1067. Vişan, Monica. “Global Well-Posedness and Scattering for the Defocusing Cubic Nonlinear Schrödinger Equation in Four Dimensions.” <i>International Mathematics Research Notices</i>, vol. 2012, no. 5, Oxford University Press, 2012, pp. 1037–67, doi:<a href="https://doi.org/10.1093/imrn/rnr051">10.1093/imrn/rnr051</a>. Vişan, Monica. “Global Well-Posedness and Scattering for the Defocusing Cubic Nonlinear Schrödinger Equation in Four Dimensions.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2012. <a href="https://doi.org/10.1093/imrn/rnr051">https://doi.org/10.1093/imrn/rnr051</a>. Vişan M. 2012. Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions. International Mathematics Research Notices. 2012(5), 1037–1067. 220752026-06-19T08:23:13Z2026-06-30T11:21:51Z