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

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

2011-12-03

arxiv.org/abs/1112.0629v1

Mathematics

Analysis of PDEs

AMS Latex, 46 pages

Scientific paper

We consider the energy-supercritical nonlinear wave equation $u_{tt}-\Delta u+|u|^2u=0$ with defocusing cubic nonlinearity in dimension $d=5$ with no radial assumption on the initial data. We prove that a uniform-in-time {\it 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 $d\geq 6$ 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.

Affiliated with

Also associated with

No associations

Rating

The defocusing energy-supercritical cubic nonlinear wave equation in dimension five does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The defocusing energy-supercritical cubic nonlinear wave equation in dimension five, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The defocusing energy-supercritical cubic nonlinear wave equation in dimension five will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-697728