Space-time analytic smoothing effect for the cubic nonlinear Schr\"odinger equations without pseudo-conformal invariance
Space-time analytic smoothing effect for the cubic nonlinear Schr\"odinger equations without pseudo-conformal invariance
复制标题
无伪共形不变性的三次非线性Schr"odinger方程的时空解析平滑效应
DOI：
10.1007/s42985-022-00151-w
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Hoshino Gaku
中科院分区：
文献类型：
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作者：
藤田 安啓;浜向 直;山口 範和;高橋仁;Hoshino Gaku;Hoshino Gaku
本文研究了空间维三次非线性薛定谔方程的整体Cauchy问题，特别证明了三次非线性薛定谔方程的时空解析光滑效应。如果立方非线性薛定谔方程在伪共形变换下是不变的，并且在这种情况下，时空解析平滑效应已经在Hoshino和Ozawa（Nonlinear Differ Equ Appl 23：3，2016）中通过应用伪共形变换的生成器进行了研究。本研究的主要目的是推广前人的研究成果。
We study the global Cauchy problem for the cubic nonlinear Schrödinger equations in space dimensionsIn particular we prove the space-time analytic smoothing effect for the cubic nonlinear Schrödinger equations. Ifthen the cubic nonlinear Schrödinger equation is invariant under the pseudo-conformal transform and in this case the space-time analytic smoothing effect has been studied in Hoshino and Ozawa (Nonlinear Differ Equ Appl 23:3, 2016) by applying the generator of pseudo-conformal transform. Our main purpose of this study is to extend the result obtained in previous study.