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Gevrey-modulation spaces and smoothing effect for the nonlinear Schrödinger equations

  • Gaku Hoshino
Article
  • 170 Downloads

Abstract

We study the global Cauchy problem for the nonlinear Schrödinger equations with the power type nonlinearity or the Hartree type nonlinearity, in the mass critical setting. Especially, we show the Gevrey smoothing effect for the nonlinear Schrödinger equations with data which satisfy sub-exponentially decaying condition and has sufficiently small norm. Also we show the existence of scattering state in the class of sub-exponentially decaying functions without loss of radius of convergence for sufficiently small data.

Notes

Acknowledgements

The author would like to thank the referees for their helpful comments and advices.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Osaka UniversityOsakaJapan

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