ABSTRACT We investigate the asymptotic behavior of solutions to the defocusing energy‐critical complex Ginzburg‐Landau equation on exterior domains and hyperbolic spaces. Employing the energy method, we establish a rigorous convergence theory for the zero‐dispersion limit from the energy‐critical complex Ginzburg‐Landau equation to the energy‐critical nonlinear heat equation. Moreover, we derive the inviscid limit connecting the energy‐critical complex Ginzburg‐Landau equation to the energy‐critical nonlinear Schrödinger equation.
Zhang et al. (Sun,) studied this question.