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• W4283827596 abstract "In this paper, we prove scattering asymptotics for the 2D (discrete dimension) cubic resonant system. This scattering result was used in Zhao [38] as an assumption to obtain the scattering for cubic NLS on R2×T2 in H1 space. Moreover, the 1D analogue is proved in Yang-Zhao [35]. Though the scheme is also tightly based on Dodson [11], the 2D case is more complicated which causes some new difficulties. One obstacle is the failure of ‘l2-estimate’ for the cubic resonances in 2D (we also discuss it in this paper, which may have its own interests). To fix this problem, we establish weaker estimates and exploit the symmetries of the resonant system to modify the proof of [35]. At last, we make a few remarks on the research line of ‘long time dynamics for NLS on waveguides’." @default.
• W4283827596 created "2022-07-07" @default.
• W4283827596 creator A5018164899 @default.
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• W4283827596 date "2023-02-01" @default.
• W4283827596 modified "2023-10-14" @default.
• W4283827596 title "On scattering asymptotics for the 2D cubic resonant system" @default.
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• W4283827596 doi "https://doi.org/10.1016/j.jde.2022.11.056" @default.
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