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

Ruipeng Shen

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arXiv · 1808.06763

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

Ruipeng Shen

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Abstract

In this short paper we consider a semi-linear, energy sub-critical, defocusing wave equation $\partial_t^2 u - \Delta u = - |u|^{p -1} u$ in the 3-dimensional space with $p \in (3,5)$. We prove that if the energy of radial initial data $(u_0, u_1)$ outside a ball of radius $r$ centred at the origin decays faster than a certain rate $r^{-\kappa(p)}$, 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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Ruipeng Shen. 2018-08-21. Morawetz Estimates Method for Scattering of Radial Energy Sub-critical Wave Equation. https://arxiv.org/abs/1808.06763

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