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

The lifespan estimates of radially symmetric solutions to systems of nonlinear wave equations in even space dimensions