We study the Cauchy problem of the mass critical nonlinear Schrödinger equation with derivative with the 4π mass. One has the global well-posedness in $H^1$ whenever “the mass is strictly less than 4π” or whenever “the mass is equal to 4π and the momentum is strictly less than zero”. In this paper, by the concentration compact principle as originally done by Kenig-Merle, we obtain the limiting profile of blow up solutions with the critical 4π mass.

中文翻译：

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最佳阈值设置下微分非线性Schrödinger方程爆破准则的注记

我们研究具有4π质量导数的质量临界非线性Schrödinger方程的Cauchy问题。一个在全球具有良好的定位$H^{\mathrm{1个}}$每当“质量严格小于4π ”或“质量等于4π并且动量严格小于零”时。在本文中，根据Kenig-Merle最初所做的浓度紧凑原理，我们获得了临界4π质量的爆炸溶液的极限轮廓。