Any results in this talk are based on a joint paper with
R. Agemi & Y. Kurokawa [1]. The existence of the critical curve
for p-q systems of nonlinear wave equations was already established by D. Del Santo & V. Georgiev & E. Mitidieri [3] except
for the critical case. Our main purpose is to prove a blow-up the
orem for which the nonlinearity (p, q) is just on the critical curve
in three space dimensions. Moreover, the lover and upper bounds
of the lifespan of solutions are precisely estimated including the
sub-critical case.
