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Space-time Gevrey smoothing effect for the dissipative nonlinear Schrödinger equations

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Abstract

We study the global Cauchy problem for the dissipative nonlinear Schrödinger equations in the setting of the fractional Sobolev space \(H^s,\)\(0<s<\min (n/2,1).\) In particular, we show the space-time Gevrey smoothing effect for global solutions to the dissipative nonlinear Scrödinger equations with data which belong to the exponential weighted Sobolev space with large norm. The proof of main theorem of this study is based on the a priori estimate for \(H^s\) solutions and a continuation method for analytic solutions has been introduced in Hoshino (J Dyn Differ Equ 4:2339–2351, 2019).

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 19K14570. The author would like to thank anonymous referees for their helpful comments and suggestions.

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  1. Division of Science, Tokyo Denki University, Hatoyama, Saitama, 350-0394, Japan

    Gaku Hoshino

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  1. Gaku Hoshino
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Correspondence to Gaku Hoshino.

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Hoshino, G. Space-time Gevrey smoothing effect for the dissipative nonlinear Schrödinger equations. Nonlinear Differ. Equ. Appl. 27, 32 (2020). https://doi.org/10.1007/s00030-020-00636-w

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