The radial defocusing energy-supercritical cubic nonlinear wave equation in R^{1+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 well-posedness 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.

AMS Latex, 20 pages

References in corpus (1)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case

Cited by in corpus (3)

• On blowup in supercritical wave equations
• Numerical simulations for the energy-supercritical nonlinear wave equation
• Scattering theory for energy-supercritical Klein-Gordon equation