Scattering of solutions to the defocusing energy subcritical semi-linear wave equation in 3D. Issue 4 (3rd April 2017)

• Record Type: Journal Article
• Authors: Shen, Ruipeng
• Is Part Of: Communications in partial differential equations. Volume 42:Issue 4(2017)
• Page Start: 495
• Page End: 518
• Publication Date: 2017-04-03
• Subjects: Energy subcriticality -- radial data -- scattering -- wave equation; 35L71 -- 35L05; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2017.1295058
• Languages: English
• ISSNs: 0360-5302

Abstract

ABSTRACT: In this paper, we consider a semi-linear, energy sub-critical, defocusing wave equation in the three-dimensional space with p ∈[3, 5). We prove that if initial data are radial so that, where dμ = (| x |+1) 1+2 𝜀 with 𝜀 >0, then the corresponding solution u must exist for all time t ∈ℝ and scatter. The key ingredients of the proof include a transformation T so that v = T u solves the equation with a finite energy, and a Morawetz-type estimate regarding a solution v as above.