The Interctitical Defocusing Nonlinear Schr?dinger Equations with Radial Initial Data in Dimensions Four and Higher

In this paper,we consider the defocusing nonlinear Schrodinger equation in space dimensions d≥4.We prove that if u is a radial solution which is priori bounded inthe critical Sobolev space,that is,u L∈Lt^∞Hx^Sc,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,Commun.PDEs,40(2015),265-308]to higher dimensions.

In this paper, we consider the defocusing nonlinear Schr?dinger 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,■, 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.