Inviscid limits of the complex Ginzburg-Landau equation

In the inviscid limit the generalized complex Ginzburg-Landau equation redu ces 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 wi th periodic boundary conditions. The results are valid for nonlinearities w ith an arbitrary growth exponent in the defocusing case and with a subcriti cal or critical growth exponent at the level of L-2 in the focusing case, i n 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.