Title

Invariance of White Noise for KdV on the Line

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.

Department(s)

Mathematics and Statistics

Comments

Article in press

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 Mar 2020

Share

 
COinS