From the abstract: We consider a nonlinear system of two-dimensional Klein-Gordon equations with masses satisfying the resonance relation . We introduce a structural condition on the nonlinearities under which the solution exists globally in time and decays at the rate as in . In particular, our new condition includes the Yukawa type interaction, which has been excluded from the null condition in the sense of J.-M. Delort, D. Fang and R. Xue [J. Funct. Anal. 211, No. 2, 288–323 (2004; Zbl 1061.35089)].
The aim in this paper is to give a new sufficient condition on the nonlinearities. Under this condition, we will show that the solution exists globally in time and it enjoys time decay property even in the resonant case.