Global well-posedness of the Benjamin-Ono equation in H^1(R)

Terence Tao

Global well-posedness of the Benjamin-Ono equation in H^1(R)

Analysis of PDEs 2007-05-23 v2

Authors: Terence Tao

Abstract

We show that the Benjamin-Ono equation is globally well-posed in $H^s(\R)$ for $s \geq 1$ . This is despite the presence of the derivative in the non-linearity, which causes the solution map to not be uniformly continuous in $H^s$ for any $s$ . The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.

Keywords

benjamin-ono equation global well-posedness gauge transformation h-sobolev space

Cite

@article{arxiv.math/0307289,
  title  = {Global well-posedness of the Benjamin-Ono equation in H^1(R)},
  author = {Terence Tao},
  journal= {arXiv preprint arXiv:math/0307289},
  year   = {2007}
}

Comments

21 pages, no figures. Minor mathematical errors corrected

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