Time decay for solutions of Schrödinger equations with rough and time-dependent potentials
Time decay for solutions of Schrödinger equations with rough and time-dependent potentials
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DOI：
10.1007/s00222-003-0325-4
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发表时间：
2001-10
影响因子：
3.1
通讯作者：
I. Rodnianski;W. Schlag
中科院分区：
文献类型：
--
作者：
I. Rodnianski;W. Schlag
本文建立了三维空间中含势线性含时Schr“odinger方程解的色散估计和Chohartz估计.我们的主要重点是小粗糙的时间依赖的潜力。这种势的例子是这样的形式，其中在时间上是准周期的，本质上是空间变量的函数。我们还证明了属于Rollnik和整体Kato类的小时间无关势的色散估计。最后，我们解决的问题所提出的关于潜在的衰减速度比Escherhartz估计。
We establish dispersive and Strichartz estimates for solutions to the linear time-dependent Schr\"odinger equations with potential in three dimensions. Our main focus is on the small rough time-dependent potentials. Examples of such potentials are of the form, whereis quasiperiodic in time andis essentially anfunction of the spatial variables. We also prove the dispersive estimates for small time-independent potentials which belong to the interestion of the Rollnik and global Kato classes. Finally, we settle the question posed by Journe, Soffer, Sogge concerning Strichartz estimates for potentials that decay faster than.