Invariance of white noise for KdV on the line

• 成果类型: Article
• 署名作者: Killip, Rowan; Murphy, Jason; Visan, Monica
• 署名单位: University of California System; University of California Los Angeles; University of Missouri System; Missouri University of Science & Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-00964-9
• 发表日期: 2020
• 页码: 203-282
• 关键词: nonlinear schrodinger-equation; global well-posedness; long-time behavior; de-vries equation; statistical-mechanics; gibbs measures; limit; MODEL

摘要

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.