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

Details The radial defocusing energy-supercritical cubic nonlinear wave equation in R^{1+5} The radial defocusing energy-supercritical cubic nonlinear wave equation in R^{1+5}

2011-04-11

arxiv.org/abs/1104.2002v1

Mathematics

Analysis of PDEs

AMS Latex, 20 pages

Scientific paper

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 Schr\"odinger equation.

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