Invariance of white noise for KdV on the line
Analysis of PDEs
2023-07-19 v1
Abstract
We consider the Korteweg--de Vries equation with white noise initial data, posed on the whole real line, and prove the almost sure existence of solutions. Moreover, we show that the solutions obey the group property and follow a white noise law at all times, past or future. As an offshoot of our methods, we also obtain a new proof of the existence of solutions and the invariance of white noise measure in the torus setting.
Keywords
Cite
@article{arxiv.1904.11910,
title = {Invariance of white noise for KdV on the line},
author = {Rowan Killip and Jason Murphy and Monica Visan},
journal= {arXiv preprint arXiv:1904.11910},
year = {2023}
}