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