Invariance of White Noise for KdV on the Line

Author

Rowan Killip
Jason Murphy, Missouri University of Science and TechnologyFollow
Monica Visan

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.

Recommended Citation

R. Killip et al., "Invariance of White Noise for KdV on the Line," Inventiones Mathematicae, vol. 222, pp. 203 - 282, Springer, Oct 2020.

The definitive version is available at https://doi.org/10.1007/s00222-020-00964-9

Department(s)

Mathematics and Statistics

Comments

Published online: 19 Mar 2020

International Standard Serial Number (ISSN)

0020-9910; 1432-1297

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2020 Springer, All rights reserved.

Publication Date

01 Oct 2020