Global scattering conjecture for one-dimensional cubic defocusing dispersive flows
In one spatial dimension, consider a dispersive flow with a cubic defocusing nonlinearity and sufficiently small initial data.
Global scattering conjecture. Such initial data should give rise to a solution that exists globally in time and scatters.
This conjecture proposes a common global well-posedness and scattering principle for one-dimensional cubic defocusing dispersive equations without any localization assumption on the initial data. The paper establishes this conclusion for particular equations, while the broad formulation remains open in general.
References
Primary source
Mihaela Ifrim and Daniel Tataru, “Global solutions for 1D cubic defocusing dispersive equations: Part I”, arXiv:2205.12212 (2023).
Additional references
23 papers in this index state this conjecture (2006–2022). The statement above is taken from the most recent of them; the others are arXiv:2108.00915, arXiv:2106.13994, arXiv:2103.15794, arXiv:1910.09805, arXiv:1808.06763, arXiv:1808.08656, arXiv:1710.09702, arXiv:1707.04686, arXiv:1604.04255, arXiv:1601.02552, arXiv:1406.2289, arXiv:1312.5427, and 10 more.
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