A note on a system of cubic nonlinear Klein-Gordon equations in one space dimension

Abstract

We study the Cauchy problem for a system of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the order $O(t^{-1/2})$ in $L^{\infty }$ as $t$ tends to infinity without the condition of a compact support on the Cauchy data which was assumed in the previous works.

22 pages

References in corpus (1)

• A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation