We study the initial-boundary vaule problem of the long and short wave equations posed on the half line with initial datas \((u_{0}, n_{0})\in H^{s_{0}}({\mathbb {R}}^{+})\times H^{s_{1}}({\mathbb {R}}^{+})\) and boundary datas \((h, f)\in H^{\frac{2s_{0}+1}{4}}({\mathbb {R}}^{+})\times H^{s_{1}}({\mathbb {R}}^{+})\) . We show the local well-posedness by giving the bilinear estimates of the coupling terms for the equations in suitable spaces of Bourgain type. Moreover, we consider results concerning ill-posedness for the system. Finally, the system is proved to be globally well-posed in Sobolev spaces \(H^{1}({\mathbb {R}}^{+})\times L^{2}({\mathbb {R}}^{+})\) .
