The global well-posedness conjecture for 1D cubic dispersive equations
Analysis of PDEs
2023-11-28 v1
Abstract
The goal of this article is to discuss a recent conjecture of the two authors, which aims to describe the long time behavior of solutions to one-dimensional dispersive equations with cubic and higher nonlinearities. These problems arguably represent the single most important example where, even for small initial data, the nonlinear effects are stronger than the dispersive effects. Consequently, the outcome predicted by the conjecture depends essentially on the structure of the nonlinearity, precisely its focusing or defocusing character.
Keywords
Cite
@article{arxiv.2311.15076,
title = {The global well-posedness conjecture for 1D cubic dispersive equations},
author = {Mihaela Ifrim and Daniel Tataru},
journal= {arXiv preprint arXiv:2311.15076},
year = {2023}
}
Comments
23 pages. This article provides an overview of the conjecture and the results in arXiv:2205.12212, arXiv:2210.17007 and arXiv:2306.00570