(untitled) (Analysis in Theory and Applications, 2019)
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, uL_t^∞ H^s_c_x, then u is global and scatters. In practice, we use weighted Strichartz space adapted for our setting which ultimately helps us solve the problems in cases d≥ 4 and 0