Existence and uniqueness of energy solution to Klein–Gordon–Schrödinger equations

This paper is concerned with the initial value problem for the nonlinear Klein–Gordon–Schrödinger (KGS) equations in R3+1 time–space. By using viscous approach, the existence of the global finite-energy solution is established for the nonlinear KGS equations by compactness argument. In addition, the uniqueness of the solution is proved by introducing a function with integral form.