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).

中文翻译：

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耗散非线性Schrödinger方程的时空Gevrey平滑效应

我们为在分数的Sobolev空间的设定的耗散非线性薛定谔方程的研究全球Cauchy问题\（H ^ S，\）\（0 <S <\分钟（N / 2,1）。\）特别是，我们给出了耗散非线性Scrödinger方程整体解的时空Gevrey平滑效应，该方程的数据属于大范数的指数加权Sobolev空间。这项研究的主要定理的证明基于\（H ^ s \）解的先验估计，并且星野引入了解析解的延续方法（J Dyn Differ Equ 4：2339–2351，2019）。