On global existence for the Schrödinger-IB system

In this paper we study global well-posedness of the Schrödinger-improved Boussinesq (S-IB) system of equations in Sobolev spaces. We prove that the one- and two-dimensional S-IB systems are globally well-posed in L2(R)×H−12(R)×H−12(R) and L2(R2)×L2(R2)×(L2(R2)∩Ḣ−1(R2)), respectively, improving the corresponding results of Ozawa and Tsutaya [T. Ozawa, K. Tsutaya, On the Cauchy problem for Schrödinger-improved Boussinesq equations, Adv. Stud. Pure Math. (in press)].