Global existence for small amplitude semilinear wave equations with
time-dependent scale-invariant damping
Global existence for small amplitude semilinear wave equations with
time-dependent scale-invariant damping
In this paper we prove a sharp global existence result for semilinear wave equations with time-dependent scale-invariant damping terms if the initial data is small. More specifically, we consider Cauchy problem of $\partial_t^2u-\Delta u+\frac{\mu}{t}\partial_tu=|u|^p$, where $n\ge 3$, $t\ge 1$ and $\mu\in(0,1)\cup(1,2)$. For critical exponent $p_{crit}(n,\mu)$ which is the positive root …