On Jensen-type Inequalities for Nonsmooth Radial Scattering Solutions of a Loglog Energy-Supercritical Schrödinger Equation

Abstract

We prove scattering of solutions of the loglog energy-supercritical Schrdinger equation [EQUATION PRESENTED] The proof uses concentration techniques (see e.g., [2, 12]) to prove a long-time Strichartz-type estimate on an arbitrarily long time interval J depending on an a priori bound of some norms of the solution, combined with an induction on time of the Strichartz estimates in order to bound these norms a posteriori (see e.g., [8, 10]). We also revisit the scattering theory of solutions with radial data in Hκ, k > nϵ , and n γ {3, 4}; more precisely, we prove scattering for a larger range of s than in [10]. In order to control the barely supercritical nonlinearity for nonsmooth solutions, that is, solutions with data in Hk, k≤n/2 , we prove some Jensen-type inequalities. © 2020 The Author(s) 2020.