In the paper, we establish the local well-posedness of the Schödinger-Boussinesq system on the half line with data of low regularity. The proof is based on the explicit solution formula of the linear boundary problem and the restricted norm method. Besides, we prove that the nonlinearity is smoother than the initial data. Our result match the known result on the full line in .
Boling Guo. Rudong Zheng. "Well-posedness of the initial-boundary value problem for the Schrödinger-Boussinesq system." Differential Integral Equations 33 (11/12) 657 - 678, November/December 2020. https://doi.org/10.57262/die/1605150096