Skip to main content
Article thumbnail
Location of Repository

THE RADIAL DEFOCUSING ENERGY-SUPERCRITICAL NONLINEAR WAVE EQUATION IN ALL SPACE DIMENSIONS

By Rowan Killip, Monica Visan and Communicated Hart F. Smith

Abstract

Abstract. We consider the defocusing nonlinear wave equation utt − Δu + |u | p 4 4 u = 0 with spherically-symmetric initial data in the regime <p< d−2 d−3 (which is energy-supercritical) and dimensions 3 ≤ d ≤ 6; we also consider d ≥ 7, but for a smaller range of p> 4 d−2. The principal result is that blowup (or failure to scatter) must be accompanied by blowup of the critical Sobolev norm. An equivalent formulation is that maximal-lifespan solutions with bounded critical Sobolev norm are global and scatter. 1

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.353.4071
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.ams.org/journals/pr... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.