In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schrödinger flows to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain smoothing effects for the non-homogeneous part of the solution can be used to upgrade to a uniform convergence to zero of this part, and we discuss the sharpness of the results obtained. We also use randomization techniques to prove that with much less regularity of the initial data, both in continuous and the periodic settings, almost surely one obtains uniform convergence of the nonlinear solution to the initial data, hence showing how more generic results can be obtained.

中文翻译：

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薛定er流的逐点收敛

在本文中，我们解决了连续和周期性设置中非线性Schrödinger流量到初始数据的几乎逐点限制的问题。然后，我们展示了在某些情况下，如何使用解决方案非均匀部分的某些平滑效果来将该部分的均匀收敛性升级为零，并讨论所获得结果的清晰度。我们还使用随机化技术来证明在连续和周期性设置中初始数据的规则性要低得多时，几乎可以肯定的是，非线性算法对初始数据的收敛性是均匀的，因此表明了如何获得更多的通用结果。