Space-time Gevrey smoothing effect for the dissipative nonlinear Schrödinger equations
Space-time Gevrey smoothing effect for the dissipative nonlinear Schrödinger equations
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DOI：
10.1007/s00030-020-00636-w
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发表时间：
2020-05
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影响因子：
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通讯作者：
G. Hoshino
中科院分区：
文献类型：
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作者：
G. Hoshino
在分数阶Sobolev空间中研究了耗散非线性Schr dinger方程的整体Cauchy问题，特别地，我们证明了具有大范数指数加权Sobolev空间的耗散非线性Schr dinger方程整体解的时空Gevrey光滑效应.本研究的主要定理的证明是基于解的先验估计，Hoshino（J Dyn Differ Equ 4：2339-2351，2019）介绍了解析解的延拓方法。
We study the global Cauchy problem for the dissipative nonlinear Schrödinger equations in the setting of the fractional Sobolev spaceIn 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 forsolutions and a continuation method for analytic solutions has been introduced in Hoshino (J Dyn Differ Equ 4:2339–2351, 2019).