On global solutions of a Zakharov type system

Abstract

We consider a class of wave-Schrodinger systems in three dimensions with a Zakharov-type coupling. This class of systems is indexed by a parameter gamma which measures the strength of the null form in the nonlinearity of the wave equation. The case gamma = 1 corresponds to the well-known Zakharov system, while the case gamma = -1 corresponds to the Yukawa system. Here we show that sufficiently smooth and localized Cauchy data lead to pointwise decaying global solutions which scatter, for any gamma is an element of (0, 1].