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Journal of Dynamics and Differential Equations

, Volume 31, Issue 4, pp 2339–2351 | Cite as

Global Well-Posedness and Analytic Smoothing Effect for the Dissipative Nonlinear Schrödinger Equations

  • Gaku HoshinoEmail author
Article

Abstract

We study the global Cauchy problem for the nonlinear Schrödinger equations in the Sobolev space of fractional order. In particular, we show the global well-posedness and the analytic smoothing effect for global solutions to a dissipative nonlinear Schrödinger equation for large data by applying a priori estimate in the Sobolev space of fractional order.

Keywords

Nonlinear Schrödinger equations Global well-posedness Sobolev space of fractional order Large data Analytic smoothing effect 

Notes

Acknowledgements

The author would like to thank the referees for their helpful comments and advices. This work was supported by JSPS KAKENHI Grant Number 17J00785.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Osaka UniversityToyonakaJapan

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