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arXiv · 2010.07821

Construction of $L^2$ log-log blowup solutions for the mass critical nonlinear Schrödinger equation

Chenjie Fan·Dana Mendelson
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Abstract

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.

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Chenjie Fan, Dana Mendelson. 2020-10-15. Construction of $L^2$ log-log blowup solutions for the mass critical nonlinear Schrödinger equation. https://arxiv.org/abs/2010.07821

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