Revisit to Fritz John's paper on the blow-up of nonlinear wave equations

In Fritz John’s famous paper (1979), he discovered that for the wave equation $\mathrm{\square }u=\mathrm{\mid }u{\mathrm{\mid }}^p$, where $1<p<1+\sqrt{2}$ and $\mathrm{\square }$ denoting the d’Alembertian, there is no global solution for any nontrivial and compactly supported initial data. This paper is intended to simplify his proof by applying a Gronwall’s type inequality.