Global well-posedness and scattering for the defocusing nonlinear Schr\"odinger equation below energy space

Abstract

In this paper, we prove global well-posedness and scattering below the energy space for the defocusing nonlinear Schr\"odinger equation with intercritical power nonlinearities in spatial dimensions $d\geq3$, improving the regularity threshold of Vi\c{s}an and Zhang [Differ. Integr. Equations, 22(2009), 99-124].