English

On invariant Gibbs measures for the generalized KdV equations

Analysis of PDEs 2016-04-27 v2 Probability

Abstract

We consider the defocusing generalized KdV equations on the circle. In particular, we construct global-in-time solutions with initial data distributed according to the Gibbs measure and show that the law of the random solutions, at any time, is again given by the Gibbs measure. In handling a nonlinearity of an arbitrary high degree, we make use of the Hermite polynomials and the white noise functional.

Keywords

Cite

@article{arxiv.1509.06873,
  title  = {On invariant Gibbs measures for the generalized KdV equations},
  author = {Tadahiro Oh and Geordie Richards and Laurent Thomann},
  journal= {arXiv preprint arXiv:1509.06873},
  year   = {2016}
}

Comments

20 pages. To appear in Dyn. Partial Differ. Equ. arXiv admin note: text overlap with arXiv:1509.02093

R2 v1 2026-06-22T11:03:22.403Z