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- W2036072016 abstract "The generalized complex Ginzburg-Landau (CGL) equation with a nonlinearity of order 2{sigma} + 1 in d spatial dimensions has a unique local classical solution for distributional initial data in the Sobolev space H{sup q} provided that q > d/2 - 1/{sigma}. This result directly corresponds to a theorem for the nonlinear Schroedinger (NLS) equation which has been proved by Cazenave and Weissler in 1990. While the proof in the NLS case relies on Besov space techniques, it is shown here that for the CGL equation, the smoothing properties of the linear semigroup can be eased to obtain an almost optimal result by elementary means. 1 fig." @default.
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- W2036072016 title "Distribution-valued initial data for the complex ginzburg-landau equation" @default.
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- W2036072016 doi "https://doi.org/10.1080/03605309708821254" @default.
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