Using the technique developed by F. Jolm in $\left[7\right]$, we
study the existence and the nonexistence of global classical solutions
to the Cauchy problem for
\[
\partial_{t}^{2}u-\Delta_{x}u=\mid v\mid^{p},
\]
\[
\partial_{t}^{2}v-\Delta_{x}v=\mid u\mid^{q},
\]
in $\mathbf{R_{\textrm{x}}^{\textrm{3}}}\times[0,+\infty[$
