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

Abstract

In this paper, we consider the defocusing nonlinear Schr ödinger 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 ∞ t Ḣs cx , 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 < s c < 1 2 .The results in this paper extend the work of [27, Commun.PDEs, 40 (2015), 265-308] to higher dimensions.

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