Inviscid limit for the energy-critical complex Ginzburg–Landau equation

In this paper, we consider the limit behavior for the solution of the Cauchy problem of the energy-critical complex Ginzburg–Landau equation in Rn, n 3. In lower dimension case (3 n 6), we show that its solution converges to that of the energy-critical nonlinear Schrödinger equation in C(0, T ,H˙ s (Rn)),T >0, s = 0, 1, as a by-product, we get the regularity of solutions in H3 for the nonlinear Schrödinger equation. In higher dimension case (n>6), we get the similar convergent behavior in C(0,T,L2(Rn)). In both cases we obtain the optimal convergent rate. © 2008 Elsevier Inc. All rights reserved