A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent

We concern the blow up problem to the scale invariant damping wave equations with sub-Strauss exponent. This problem has been studied by Lai, Takamura and Wakasa (cite{Lai17}) and Ikeda and Sobajima cite{Ikedapre} recently. In present paper, we extend the blowup exponent from $p_F(n)leq p<p_S(n+2mu)$ to $1<p<p_S(n+mu)$ without small restriction on $mu$. Moreover, the upper bound of lifespan is derived with uniform estimate $T(varepsilon)leq Cvarepsilon^{-2p(p-1)/gamma(p,n+2mu)}$. This result extends the blowup result of semilinear wave equation and shows the wave-like behavior of scale invariant damping wave equations solution even with large $mu>1$.