Global well-posedness for the generalized 2D Ginzburg–Landau equation

The local well-posedness for the generalized two-dimensional (2D) Ginzburg–Landau equation is obtained for initial data in Hs(R2) (s>1/2). The global result is also obtained in Hs(R2) (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.