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

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#### 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.