Well-posedness for the Schrödinger-Improved Boussinesq System and Related Bilinear Estimates

Abstract

We consider the Cauchy problem for the Schrödinger-improved Boussinesq system. We prove the local well-posedness below L² and the global one in L². The main ingredient for the local well-posedness is nearly optimal bilinear estimates related with the Schrödinger-improved Boussinesq system in the Bourgain space X^s,b.