Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrodinger equation

• 成果类型: Article
• 署名作者: Oh, Tadahiro; Tzvetkov, Nikolay
• 署名单位: University of Edinburgh; Heriot Watt University; University of Edinburgh; CY Cergy Paris Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0748-7
• 发表日期: 2017
• 页码: 1121-1168
• 关键词: global well-posedness; long-time behavior; gibbs measure; differential-equations; statistical-mechanics; cauchy-problem; ill-posedness; wave-equation; unit ball; kdv

摘要

We consider the cubic fourth order nonlinear Schrodinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces , , are quasi-invariant under the flow.