|
|
楼主 |
发表于 2024-3-23 22:17:00
来自手机
|
显示全部楼层
xierbote 发表于 2024-3-23 22:09
上海科技大学岳海天一篇annals of math
Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two
From To appear in forthcoming issues by Yu Deng, Andrea R. Nahmod, Haitian Yue
Abstract
We consider the defocusing nonlinear Schrödinger equation on T2 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.
Milestones
Received: 29 October 2019
Revised: 5 July 2023
Accepted: 20 March 2024
Authors
Yu Deng
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
Andrea R. Nahmod
Department of Mathematics, University of Massachusetts, Amherst, MA 01003, USA
Haitian Yue
Institute of Mathematical Sciences, ShanghaiTech University, Shanghai 201210, China |
|
[复制链接]
发表于 2024-1-22 10:58:57
发表于 2024-1-22 11:40:47
