Invariance of White Noise for KdV on the Line
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.
R. Killip et al., "Invariance of White Noise for KdV on the Line," Inventiones Mathematicae, Springer, Mar 2020.
The definitive version is available at https://doi.org/10.1007/s00222-020-00964-9
Mathematics and Statistics
International Standard Serial Number (ISSN)
Article - Journal
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01 Mar 2020