The Intercritical Defocusing Nonlinear Schrödinger Equations with Radial Initial Data in Dimensions Four and Higher (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, $u\in L_t^∞ \dot{H}^{s_c}_x$, 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