Invariant Gibbs measures and global strong solutions for nonlinear Schrodinger equations in dimension two

• 成果类型: Article
• 署名作者: Deng, Yu; Nahmod, Andrea R.; Yue, Haitian
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2024.200.2.1
• 发表日期: 2024
• 页码: 399-486
• 关键词: local well-posedness; long-time behavior; data cauchy-theory; statistical-mechanics; wave-equations; unit ball; RENORMALIZATION; triviality; SCATTERING

摘要

We consider the defocusing nonlinear Schrodinger equation on T-2 with Wick ordered power nonlinearity, and prove almost sure global well-posedness with respect to the associated Gibbs measure. The heart of the matter is the uniqueness of the solution as limit of solutions to canonically truncated systems, and the invariance of the Gibbs measure under the global dynamics follows as a consequence. The proof relies on the novel idea of random averaging operators.