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