The radial defocusing energy-supercritical cubic nonlinear wave equation in $\mathbb{R}^{{\sf 1}+{\sf 5}}$

Abstract

In this work, we consider the energy-supercritical defocusing cubic nonlinear wave equation in dimension d = 5 for radially symmetric initial data.We prove that an a priori bound in the critical space implies global wellposedness and scattering.The main tool that we use is a frequency localized version of the classical Morawetz inequality, inspired by recent developments in the study of the mass and energy critical nonlinear Schrödinger equation.

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