The defocusing energy-critical nonlinear Schr\"odinger equation in higher dimensions

TL;DR

This paper proves global well-posedness and scattering for the energy-critical nonlinear Schrödinger equation in higher dimensions, establishing spacetime bounds for energy solutions in dimensions five and above.

Contribution

It extends the understanding of the defocusing energy-critical NLS to higher dimensions, providing new results on global behavior and spacetime bounds.

Findings

Global well-posedness established for n≥5

Scattering results proven for energy solutions

Global spacetime bounds in critical Lebesgue spaces

Abstract

We obtain global well-posedness, scattering, and global $L^{\frac{2(n+2)}{n-2}}_{t,x}$ spacetime bounds for energy-space solutions to the energy-critical nonlinear Schr\"odinger equation in $\R_t\times \R^n_x$, $n\geq 5$.