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# Global well-posedness of the Cauchy problem for nonlinear Schrödinger-type equations

• In this paper the global well-posedness in $L^2$ and $H^m$ of the Cauchy problem is proved for nonlinear Schrödinger-type equations. This we do by establishing regular Strichartz estimates for the corresponding linear equations and some nonlinear a priori estimates in the framework of Besov spaces. We further establish the regularity of the $H^m$-solution to the Cauchy problem.
Mathematics Subject Classification: Primary: 35Q55, 37L05.

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