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

Abstract

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 $p_F(n)\le p<p_S(n+2\mu )$ to $1<p<p_S(n+\mu )$ without small restriction on $\mu$. Moreover, the upper bound of lifespan is derived with uniform estimate $T(\epsilon )\le C{\epsilon }^{-2p(p-1)/\gamma (p,n+2\mu )}$. This result extends the blowup result of semilinear wave equation and shows the wave-like behavior of scale invariant damping wave equation's solution even with large $\mu >1$.

References in corpus (1)

• Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data

Cited by in corpus (2)

• New blow-up result for the weakly coupled wave equations with a scale-invariant damping and time derivative nonlinearity
• Small data blow-up for the wave equation with a time-dependent scale invariant damping and a cubic convolution for slowly decaying initial data