Wellposedness in energy space for the nonlinear Klein–Gordon–Schrödinger system

This paper is concerned with the wellposedness of the nonlinear Klein–Gordon–Schrödinger (NKGS) equations under multi-interactions in 3 dimensions. By using the vanishing viscosity techniques and the compactness arguments, we establish the existence of the global finite energy solutions for the NKGS equations. In addition, by introducing a time piecewise function with integral form, we prove uniqueness and continuous dependence on the initial data.