Remarks on the asymptotic behavior of global solutions to systems of semilinear wave equations

Abstract

We consider the Cauchy problem for systems of semilinear wave equations with small initial data in two and three space dimensions. We first present some recent results on the global existence and the asymptotic behavior of solutions under weaker conditions than the so-called null condition. Then, restricting our attention to two-component systems with nonlinearity of the critical power, we will discuss the asymptotic behavior in more details, and show that the asymptotic behavior observed in two space dimensions can be more complicated than that in three space dimensions.