Blow-up Dynamics for L2-Critical Fractional Schrödinger Equations

DOI10.1093/IMRN/RNAB086zbMATH Open1498.35507arXiv1908.09561OpenAlexW3165121259MaRDI QIDQ5038048

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Publication date: 29 September 2022

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Abstract: In this paper, we will consider the $L^2$-critical fractional Schr"odinger equation $$ with initial data $$ and $$ close to $2$. We will show that the solution blows up in finite time if the initial data has negative energy and slightly supercritical mass. We will also give a specific description for the blow-up dynamics. This is an extension of the work of F. Merle and P. Rapha"el for $L^2$-critical Schr"odinger equations but the nonlocal structure of this equation and the lack of some symmetries make the analysis more complicated, hence some new strategies are required.

Full work available at URL: https://arxiv.org/abs/1908.09561

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