Global existence for a Zakharov type system in a domain

Abstract

We study an initial-boundary value problem for a Zakharov type system in three space dimensions in a general domain. Under a smallness assumption on the initial data, we construct a unique global strong solution. The solution is obtained by a direct approach based on higher-order energy estimates and the construction of a Cauchy sequence in suitable Banach spaces, without employing compactness methods. Furthermore, we obtain estimates on the growth of higher-order Sobolev norms of solutions.