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

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 $2<p\le \frac{1+\sqrt{17}}{2}$, the solution still decays with rate at least $t^{-\frac{1}{3}}$. As a consequence, the solution scatters in energy space when $p>2.3542$. We also show that the solution is uniformly bounded when $p>\frac{3}{2}$.

arXiv comment37 pages, combined the results in arXiv.1910.02230

References in corpus (4)

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• A new physical-space approach to decay for the wave equation with applications to black hole spacetimes
• On the quasilinear wave equations in time dependent inhomogeneous media
• Large data pointwise decay for defocusing semilinear wave equations

Cited by in corpus (6)

• Pointwise decay for the wave equation on nonstationary spacetimes
• Decay estimates for the massless Vlasov equation on Schwarzschild spacetimes
• Uniform bound for solutions of semilinear wave equations in ${\mathbb{R}}^{1+3}$
• On the global behaviors for defocusing semilinear wave equations in ${\mathbb{R}}^{1+2}$
• Asymptotic decay for defocusing semilinear wave equations in ${\mathbb{R}}^{1+1}$
• On the defocusing semilinear wave equations in three space dimension with small power