论文标题
$ l^2 $ log-log爆炸解决方案用于质量关键的非线性schrödinger方程
Construction of $L^2$ log-log blowup solutions for the mass critical nonlinear Schrödinger equation
论文作者
论文摘要
在本文中，我们研究了$ \ Mathbb {r}^{2} $在$ l^{2}（\ Mathbb {r}^2）$ l^{2}（\ Mathbb {r}^2）$ juropartion的$ \ mathbb {r}^{2} $上的质量关键非线性schrödinger方程的日志爆炸动力学。特别是，通过采用概率方法，我们提供了$ l^{2}（\ Mathbb {r}^2）的家庭的构造，这些解决方案不在任何$ h^{s}（\ Mathbb {r}^2）$中，任何$ h^{s} $ s> 0 $，以及根据log-log log log log log-log log log log log log log log log log log log log log log log log log log log log log log log log log。
In this article, we study the log-log blowup dynamics for the mass critical nonlinear Schrödinger equation on $\mathbb{R}^{2}$ under rough but structured random perturbations at $L^{2}(\mathbb{R}^2)$ regularity. In particular, by employing probabilistic methods, we provide a construction of a family of $L^{2}(\mathbb{R}^2)$ regularity solutions which do not lie in any $H^{s}(\mathbb{R}^2)$ for any $s>0$, and which blowup according to the log-log dynamics.
