In this paper the global well-posedness in L² and Hᵐ of the Cauchy problemis proved for nonlinear Schrödinger-type equations. This we do by establishingregular Strichartz estimates for the corresponding linear equations and some nonlineara priori estimates in the framework of Besov spaces. We further establishthe regularity of the Hᵐ-solution to the Cauchy problem.
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Miao et al. (2007) studied this question.