Invariance of white noise for KdV on the line
Killip R, Murphy J, Vişan M. 2020. Invariance of white noise for KdV on the line. Inventiones mathematicae. 222(1), 203–282.
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Author
Killip, Rowan;
Murphy, Jason;
Vişan, MonicaISTA
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.
Publishing Year
Date Published
2020-10-01
Journal Title
Inventiones mathematicae
Publisher
Springer Nature
Volume
222
Issue
1
Page
203-282
ISSN
eISSN
IST-REx-ID
Cite this
Killip R, Murphy J, Vişan M. Invariance of white noise for KdV on the line. Inventiones mathematicae. 2020;222(1):203-282. doi:10.1007/s00222-020-00964-9
Killip, R., Murphy, J., & Vişan, M. (2020). Invariance of white noise for KdV on the line. Inventiones Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-020-00964-9
Killip, Rowan, Jason Murphy, and Monica Vişan. “Invariance of White Noise for KdV on the Line.” Inventiones Mathematicae. Springer Nature, 2020. https://doi.org/10.1007/s00222-020-00964-9.
R. Killip, J. Murphy, and M. Vişan, “Invariance of white noise for KdV on the line,” Inventiones mathematicae, vol. 222, no. 1. Springer Nature, pp. 203–282, 2020.
Killip R, Murphy J, Vişan M. 2020. Invariance of white noise for KdV on the line. Inventiones mathematicae. 222(1), 203–282.
Killip, Rowan, et al. “Invariance of White Noise for KdV on the Line.” Inventiones Mathematicae, vol. 222, no. 1, Springer Nature, 2020, pp. 203–82, doi:10.1007/s00222-020-00964-9.
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