English

Global rough solutions to the critical generalized KdV equation

Analysis of PDEs 2010-09-30 v2

Abstract

We prove that the initial value problem (IVP) for the critical generalized KdV equation ut+uxxx+(u5)x=0u_{t}+u_{xxx}+(u^5)_{x}=0 on the real line is globally well-posed in Hs(R)H^{s}(\R) provided s>3/5s>3/5.

Cite

@article{arxiv.0908.0344,
  title  = {Global rough solutions to the critical generalized KdV equation},
  author = {Luiz Gustavo Farah},
  journal= {arXiv preprint arXiv:0908.0344},
  year   = {2010}
}

Comments

23 pages, no figures. References updated, some comments added after Proposition 3.1, typos fixed. Submitted for publication

R2 v1 2026-06-21T13:32:03.553Z