The low regularity global solutions for the critical generalized KdV equation
Analysis of PDEs
2020-05-08 v3 Mathematical Physics
math.MP
Abstract
We prove that the Cauchy problem of the mass-critical generalized KdV equation is globally well-posed in Sobolev spaces for . Of course, we require that the mass is strictly less than that of the ground state in the focusing case. The main approach is the "I-method" together with the multilinear correction analysis. Moreover, we use some "partially refined" argument to lower the upper control of the multiplier in the resonant interactions. The result improves the previous works of Fonseca, Linares, Ponce (2003) and Farah (2009).
Cite
@article{arxiv.0908.0782,
title = {The low regularity global solutions for the critical generalized KdV equation},
author = {Changxing Miao and Shuanglin Shao and Yifei Wu and Guixiang Xu},
journal= {arXiv preprint arXiv:0908.0782},
year = {2020}
}
Comments
27pages, the mistake in the previous version is corrected; using I-method with the resonant decomposition gives an improvement over our previous results