Abstract
The local well-posedness for the generalized two-dimensional (2D) Ginzburg–Landau equation is obtained for initial data in H s ( R 2 ) ( s > 1 / 2 ) . The global result is also obtained in H s ( R 2 ) ( s > 1 / 2 ) under some conditions. The results on local and global well-posedness are sharp except the endpoint s = 1 / 2 . We mainly use the Tao's [ k ; Z ] -multiplier method to obtain the trilinear and multilinear estimates.
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