Morawetz Estimates Method for Scattering of Radial Energy Sub-critical Wave Equation

2018/08/21 by Shen, Ruipeng
#35L05 #35L71 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.06763

Abstract

In this short paper we consider a semi-linear, energy sub-critical, defocusing wave equation ∂_t² u - Δu = - |u|^{p -1} u in the 3-dimensional space with p ∈ (3,5). We prove that if the energy of radial initial data (u₀, u₁) outside a ball of radius r centred at the origin decays faster than a certain rate r^-κ(p), then the corresponding solution u must scatter in both two time directions. The main tool of our proof is a more detailed version of the classic Morawetz estimate.

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