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On Jensen-type inequalities for unbounded radial scattering solutions of a loglog energy-supercritical Schrodinger equation

Research paper by Tristan Roy

Indexed on: 20 Sep '17Published on: 20 Sep '17Published in: arXiv - Mathematics - Analysis of PDEs



Abstract

Given $n \in \{ 3,4 \} (resp. n=5) and k > 1$ (resp. $\frac{4}{3} > k > 1$), we prove scattering of the radial $\tilde{H}^{k}:= \dot{H}^{k}(\mathbb{R}^{n}) \cap \dot{H}^{1}(\mathbb{R}^{n})$ solutions of the loglog energy-supercritical Schrodinger equation $i \partial_{t} u + \triangle u = |u|^{\frac{4}{n-2}}u log^{\gamma} (\log( 10 + |u|^{2} ))$ for $0 < \gamma < \gamma_{n}$. In order to deal with the barely supercritical nonlinearity for unbounded solutions, i.e solutions with data in $\tilde{H}^{k}, k \leq \frac{n}{2}$, we prove some Jensen-type inequalities.