Analytic smoothing effect for global solutions to a quadratic system of nonlinear Schr?dinger equations
Analytic smoothing effect for global solutions to a quadratic system of nonlinear Schr?dinger equations
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非线性薛定谔方程二次系统全局解的解析平滑效应
DOI：
10.1007/s00030-017-0486-2
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Gaku Hoshino
中科院分区：
文献类型：
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作者：
Hoshino Gaku;Hoshino Gaku;Gaku Hoshino;Gaku Hoshino
本文研究了非线性薛定谔方程组在次临界和尺度临界Sobolev情形下的Cauchy问题。特别地，我们通过应用Sasaki（J Funct Anal 270：1064-1090，2016）研究的方法和Hayashi等人（Ann Inst Henri Poincaré-AN 30：661-690，2013）证明的质量守恒定律，研究了非线性薛定谔方程组在质量共振条件下的空间变量中的解析平滑效应，其中大数据满足空间无穷大的指数衰减条件。在尺度临界Sobolev背景下，当数据具有充分小的范数且在空间无穷远处满足指数衰减条件时，讨论了空间变量的解析光滑效应。
We consider the Cauchy problem for a system of nonlinear Schrödinger equations in the-subcritical setting or in the scale critical Sobolev setting. In particular, we study analytic smoothing effect in space variables for a system of nonlinear Schrödinger equations under the mass resonance condition by applying the method has been studied in Sasaki (J Funct Anal 270:1064–1090, 2016) and the mass conservation law has been proved in Hayashi et al. (Ann Inst Henri Poincaré-AN 30:661–690, 2013), with large data which satisfy exponentially decaying condition at spatial infinity. Also we discus analytic smoothing effect in space variables in the scale critical Sobolev setting with data which have sufficiently small norm and satisfy exponentially decaying condition at spatial infinity.