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,the...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.展开更多
基金supported in part by the National Natural Science Foundation of China under grant No.11671047 and No.11726005supported by the LabEx MME-DII
文摘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.
