MathDBGlobal scattering conjecture for one-dimensional cubic defocusing dispersive flows
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.
Sources & referencesView supporting material
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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