Construction of $L^2$ log-log blowup solutions for the mass critical nonlinear Schr\'odinger equation
| Autor: | Fan, Chenjie, Mendelson, Dana |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this article, we study the log-log blowup dynamics for the mass critical nonlinear Schr\"odinger 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. Comment: 47 pages. All comments are welcome |
| Databáze: | arXiv |
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