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• W4376122812 abstract "In this paper, we succeed in integrating Strichartz estimates (encoding the dispersive effects of the equations) in Birkhoff normal form techniques. As a consequence, we deduce a result on the long time behavior of quintic NLS solutions on the circle for small but very irregular initial data (in $H^s$ for $s > 2/5$). Note that since $2/5 < 1$, we cannot claim conservation of energy and, more importantly, since $2/5 < 1/2$, we must dispense with the algebra property of $H^s$. This is the first dynamical result where we use the dispersive properties of NLS in a context of Birkhoff normal form." @default.
• W4376122812 created "2023-05-12" @default.
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• W4376122812 date "2023-05-09" @default.
• W4376122812 modified "2023-10-17" @default.
• W4376122812 title "Dynamics of quintic nonlinear Schr{o}dinger equations in $H^{2/5+}(mathbb{T})$" @default.
• W4376122812 doi "https://doi.org/10.48550/arxiv.2305.05236" @default.
• W4376122812 hasPublicationYear "2023" @default.
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