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

Abstract 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 H 1 is also obtained and the decaying rate is independent of time t∈[0,∞).

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