  The optimal lifespan estimates of a solution to weakly coupled systems of
wave equations have been investigated by many works, except for the lower bound
in even space dimensions. Our aim is to prove the open part under the
assumption of radial symmetry on the solution. The odd dimensional case was
already obtained in our previous paper by long time existence of the solution
in weighted $L^\infty$ space. In this paper, we employ similar methods. The
main difficulty is found in estimating the integral kernel which is completely
different from odd dimensional case.
