(untitled) (Journal of Partial Differential Equations, 2022)
In this paper we prove that the Schrödinger-Boussinesq system with solution (u,v, (-_xx)^-12 v_t) is locally wellposed in H^s× H^s× H^s-1, s-1/4. The local wellposedness is obtained by the transformation from the problem into a nonlinear Schrödinger type equation system and the contraction mapping theorem in a suitably modified Bourgain type space inspired by the work of Kishimoto, Tsugawa. This result improves the known local wellposedness in H^s× H^s× H^s-1, s>-1/4 given by Farah.