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arXiv · 1908.00607

Pointwise decay for semilinear wave equations in $\mathbb{R}^{!+3}$

Shiwu Yang
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Abstract

In this paper, we use Dafermos-Rodnianski's new vector field method to study the asymptotic pointwise decay properties for solutions of energy subcritical defocusing semilinear wave equations in $\mathbb{R}^{1+3}$. We prove that the solution decays as quickly as linear waves for $p>\frac{1+\sqrt{17}}{2}$, covering part of the sub-conformal case, while for the range $2 2.3542$. We also show that the solution is uniformly bounded when $p>\frac{3}{2}$.

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BibTeXRIS

Shiwu Yang. 2019-08-01. Pointwise decay for semilinear wave equations in $\mathbb{R}^{!+3}$. https://arxiv.org/abs/1908.00607

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