On Global Smooth Solution of a Semi-linear System of Wave Equations in R3

Abstract

In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth solution of the systemfor subcritical case by using conservation of energy and Strichartz's estimate. On the basis ofMorawetz-Poho\check{z}ev identity, we obtain the same result for the critical case.