We prove that solution of defocusing semilinear wave equation in $\mathbb{ R}^{ 1+3}$ with pure power nonlinearity is uniformly bounded for all $\frac{ 3}{ 2}<p\leq 2$ with sufficiently smooth and localized data. The result relies on the $r$-weighted energy estimate originally introduced by Dafermos and Rodnianski. This appears to be the first result regarding the global asymptotic property for the solution with small power $p$ under 2.
Categories: math.AP