  In this paper, complex Ginzburg-Landau (CGL) equations with superlinear
growth terms are studied. We discuss the local well-posedness in the energy
space H1 for the initial-boundary value problem of the equations in general
domains. The local well-posedness in H1 in bounded domains is already examined
by authors (2019). Our approach to CGL equations is based on the theory of
parabolic equations governed by subdifferential operators with non-monotone
perturbations. By using this method together with the Yosida approximation
procedure, we discuss the existence and the uniqueness of local solutions as
well as the global existence of solutions with small initial data.
