Well‐posedness of initial‐boundary value problem for a coupled Benjamin–Bona–Mahony–Schrödinger system

Abstract

We derive the well‐posedness results concerning the initial‐boundary value problem for a class of coupled Benjamin–Bona–Mahony (BBM)–Schrödinger system. More precisely, we obtain the existence of local smooth solutions of (1) for initial and boundary data in the energy space Hm × Hm for . Depending on a priori estimates, we also prove that the solutions exist global in time in the energy space H2 × H2.