Global smooth solution for the Klein–Gordon–Zakharov equations

Abstract

In this paper the initial value problem to the Klein–Gordon–Zakharov equations in two dimensions is discussed. Without assuming that the Cauchy data are small, we prove the existence and uniqueness of the global smooth solution for the problem via the so-called continuous method and delicate a priori estimates. Also the asymptotic behaviour of the solution to the K–G–Z equations with a small parameter approaching zero is studied.