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We prove scattering of $\tilde{H}^{k} $ solutions of the loglogenergy-supercritical Schrodinger equation $i \partial_{t} u + \triangle u =|u|^{\frac{4}{n-2}} u \log^{c} {(\log{(10+|u|^{2})})}$, $0 < c < c_{n}$,$n={3,4}$, with radial data $u(0):=u_{0} \in \tilde{H}^{k} $, $k>n/2$. This isachieved, roughly speaking, by extending Bourgain's argument (see alsoGrillakis) and Tao's argument in high dimensions.

Scattering above energy norm of solutions of a loglog energy-supercritical Schrodinger equation with radial data