The interctitical defocusing nonlinear Schrödinger equations with radial initial data in dimensions four and higher

Abstract

In this paper, we consider the defocusing nonlinear Schrödinger equation in space dimensions $d\ge 4$. We prove that if $u$ is a radial solution which is \emph{priori} bounded in the critical Sobolev space, that is, $u\in L_t^{\infty }{\dot{H}}_x^{s_c}$, 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 $d\ge 4$ and $0<s_c<\f{1}{2}$. The results in this paper extend the work of \cite[Comm. in PDEs, 40(2015), 265-308]{M3} to higher dimensions.

25pages

References in corpus (5)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• Global well-posedness and scattering for the defocusing, $L^2$-critical, nonlinear Schr{ö}dinger equation when $d=2$
• Global well - posedness and scattering for the focusing, energy - critical nonlinear Schrödinger problem in dimension $d=4$ for initial data below a ground state threshold
• The radial defocusing energy-supercritical NLS in dimension four
• The defocusing energy-supercritical NLS in four space dimensions