On the Convergence of the Complex Ginzburg‐Landau Equation on Some Riemannian Manifolds

Key Points

• The aim is to study the asymptotic behavior of solutions to the complex Ginzburg‐Landau equation on specific manifolds.
• Application of the energy method for analysis.
• Investigation of zero‐dispersion limits in exterior domains and hyperbolic spaces.
• Derivation of inviscid limits connecting different energy‐critical equations.
• Rigorous convergence theory established for the transition from complex Ginzburg‐Landau to nonlinear heat equation.
• Connection derived between complex Ginzburg‐Landau and nonlinear Schrödinger equations.

Abstract