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The Cauchy Problem of the Nonlinear Schrödinger Equations in ℝ1+1

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Abstract

In this paper, we consider the local and global solution for the nonlinear Schrödinger equation with data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data. The techniques to be used are adapted from the Strichartz type estimate, Kato’s smoothing effect and the maximal function (in time) estimate for the free Schrödinger operator.

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  1. Institute of Applied Physics and Computational Mathematics, 8009, Beijing, 100088, China

    Gui-xiang Xu

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  1. Gui-xiang Xu
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Xu, Gx. The Cauchy Problem of the Nonlinear Schrödinger Equations in ℝ1+1 . Acta Mathematicae Applicatae Sinica, English Series 23, 593–610 (2007). https://doi.org/10.1007/s10255-007-0398

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  • DOI: https://doi.org/10.1007/s10255-007-0398

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