The Intercritical Defocusing Nonlinear Schrödinger Equations with Radial Initial Data in Dimensions Four and Higher

Abstract

In this paper, we consider the defocusing nonlinear Schrödinger equation in space dimensions d ≥ 4. We prove that if u is a radial solution which is priori bounded in the critical Sobolev space, that is, u ∈ L ∞ tḢ sc x , then u is global and scatters. In practise, we use weighted Strichartz space adapted for our setting which ultimately helps us solve the problems in cases d ≥ 4 and 0 < sc < 1 2 . The results in this paper extend the work of [27, Comm. in PDEs, 40(2015), 265-308] to higher dimensions.

On scattering for the defocusing high dimensional inter-critical NLS

“…Then, J. Murphy in [26] extended the analogous result to d ≥ 4. See also [13,25,37,38] for other inter-critical results. As for energy-supercritical case, we refer to [11,23,19,24,27].…”