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

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 $i{\partial }_{t}u+△u=|u{|}^{\frac{4}{n-2}}ulo{g}^{\gamma }(\log (10+|u{|}^2))$ for $0<\gamma <{\gamma }_n$. In order to control the barely supercritical nonlinearity for nonsmooth solutions, i.e solutions with data in ${\tilde{H}}^k$, $k\le \frac{n}{2}$, we prove some Jensen-type inequalities.

arXiv comment32 pages. Title slightly changed. Version similar to published version