The global well-posedness and spatial decay of solutions for the derivative complex Ginzburg–Landau equation in H1 Original Research Article

The global well-posedness for the Cauchy problem of the derivative complex Ginzburg–Landau equation is shown in the H1-critical and H1-subcritical cases. A spatial decaying estimate of solutions in View the MathML source is also obtained and the decaying rate is independent of time t∈[0,∞).