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The Cauchy problem in local spaces for the complex Ginzburg-Landau equation. II: Contraction methods. (English) Zbl 0889.35046
The present paper is a continuation of the previous work of the same authors [Physica D, 191-228 (1995; reviewed above)]. Treating the same problems by means of contraction methods, the authors prove the uniqueness of solutions under some subcriticality conditions, and obtain additional regularity properties and uniform bounds.

35K55 Nonlinear parabolic equations
35K15 Initial value problems for second-order parabolic equations
35Q55 NLS equations (nonlinear Schrödinger equations)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
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