The defocusing energy-supercritical cubic nonlinear wave equation in dimension five

Document Type

Article

Publication Date

1-1-2015

Abstract

We consider the energy-supercritical nonlinear wave equation utt− Δu + |u|2u = 0 with defocusing cubic nonlinearity in dimension d = 5 with no radial assumption on the initial data. We prove that a uniform-in-time a priori bound on the critical norm implies that solutions exist globally in time and scatter at infinity in both time directions. Together with our earlier works in dimensions d ≥ 6 with general data and dimension d = 5 with radial data, the present work completes the study of global well-posedness and scattering in the energy-supercritical regime for the cubic nonlinearity under the assumption of uniform-in-time control over the critical norm.

Publication Source (Journal or Book title)

Transactions of the American Mathematical Society

First Page

6017

Last Page

6061

This document is currently not available here.

Share

COinS