{"_id":"22054","arxiv":1,"scopus_import":"1","month":"10","citation":{"apa":"Killip, R., Murphy, J., &#38; Vişan, M. (2020). Invariance of white noise for KdV on the line. <i>Inventiones Mathematicae</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00222-020-00964-9\">https://doi.org/10.1007/s00222-020-00964-9</a>","ama":"Killip R, Murphy J, Vişan M. Invariance of white noise for KdV on the line. <i>Inventiones mathematicae</i>. 2020;222(1):203-282. doi:<a href=\"https://doi.org/10.1007/s00222-020-00964-9\">10.1007/s00222-020-00964-9</a>","ieee":"R. Killip, J. Murphy, and M. Vişan, “Invariance of white noise for KdV on the line,” <i>Inventiones mathematicae</i>, vol. 222, no. 1. Springer Nature, pp. 203–282, 2020.","ista":"Killip R, Murphy J, Vişan M. 2020. Invariance of white noise for KdV on the line. Inventiones mathematicae. 222(1), 203–282.","chicago":"Killip, Rowan, Jason Murphy, and Monica Vişan. “Invariance of White Noise for KdV on the Line.” <i>Inventiones Mathematicae</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00222-020-00964-9\">https://doi.org/10.1007/s00222-020-00964-9</a>.","mla":"Killip, Rowan, et al. “Invariance of White Noise for KdV on the Line.” <i>Inventiones Mathematicae</i>, vol. 222, no. 1, Springer Nature, 2020, pp. 203–82, doi:<a href=\"https://doi.org/10.1007/s00222-020-00964-9\">10.1007/s00222-020-00964-9</a>.","short":"R. Killip, J. Murphy, M. Vişan, Inventiones Mathematicae 222 (2020) 203–282."},"publication_status":"published","volume":222,"type":"journal_article","OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","article_type":"original","oa":1,"issue":"1","date_published":"2020-10-01T00:00:00Z","publisher":"Springer Nature","language":[{"iso":"eng"}],"doi":"10.1007/s00222-020-00964-9","year":"2020","quality_controlled":"1","das_tickbox":"1","external_id":{"arxiv":["1904.11910"]},"page":"203-282","OA_type":"green","title":"Invariance of white noise for KdV on the line","day":"01","intvolume":"       222","date_updated":"2026-06-25T08:39:30Z","oa_version":"Preprint","abstract":[{"lang":"eng","text":"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."}],"author":[{"full_name":"Killip, Rowan","last_name":"Killip","first_name":"Rowan"},{"last_name":"Murphy","full_name":"Murphy, Jason","first_name":"Jason"},{"last_name":"Visan","full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}],"article_processing_charge":"No","status":"public","date_created":"2026-06-19T07:56:16Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1904.11910"}],"publication":"Inventiones mathematicae","publication_identifier":{"eissn":["1432-1297"],"issn":["0020-9910"]}}