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.
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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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Hoshino, G. Global Well-Posedness and Analytic Smoothing Effect for the Dissipative Nonlinear Schrödinger Equations. J Dyn Diff Equat 31, 2339–2351 (2019). https://doi.org/10.1007/s10884-018-9709-4
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DOI: https://doi.org/10.1007/s10884-018-9709-4