Inviscid Limits of the Complex Ginzburg-Landau Equation

In the inviscid limit the generalized complex Ginzburg-Landau equation reduces to the nonlinear Schrodinger equation. This limit is proved rigorously with H 1 data in the whole space for the Cauchy problem and in the torus with periodic boundary conditions. The results are valid for nonlinearities with subcritical or critical growth exponent at the level of H 1 in any spatial dimension. Furthermore, optimal convergence rates are proved. The proofs are based on estimates of the Schrodinger energy functional and on Gagliardo-Nirenberg inequalities. Keywords. Generalized complex Ginzburg-Landau equation, nonlinear Schrodinger equation, energy estimates, optimal rate of convergence, strong solutions. 1991 Mathematics Subject Classification. 35K55, 35Q55, 81Q05. Acknowledgments. The authors acknowledge support from the DAAD-PROCOPE Program, the DAAD `Acciones Integradas' Program, and from the TMR Project "Asymptotic Methods in Kinetic Theory", grant number ERB-FMBX-CT97-0157. The seco..