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xierbote 发表于 2024-3-23 22:090 a% d# v% J$ u: o- k
上海科技大学岳海天一篇annals of math
# X. r1 K- f3 y4 gInvariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two- O' H6 L6 C: s4 m
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From To appear in forthcoming issues by Yu Deng, Andrea R. Nahmod, Haitian Yue
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Abstract2 x2 i- f+ J- Q5 J
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.( R" H' e" Q) L. Z
7 d, Z! H9 c% v- J9 }- \Milestones
+ ^$ Z& n. T6 k7 u2 nReceived: 29 October 2019
( ]3 r- Q6 l6 c1 W, QRevised: 5 July 2023
2 k7 ?5 x% i5 e' C- K6 H2 tAccepted: 20 March 2024' M3 e! u9 h/ ]6 L) k2 N
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Authors
- ~7 X! s+ N3 ?8 J8 _Yu Deng
4 I3 \# c" _: T9 Z6 b6 y5 jDepartment of Mathematics, University of Southern California, Los Angeles, CA 90089, USA6 t0 e4 T; n, a8 u* F
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Andrea R. Nahmod0 n: X V$ |, h' t( H7 a7 `' K
Department of Mathematics, University of Massachusetts, Amherst, MA 01003, USA
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Haitian Yue
$ f' \% a! E( ]( ^Institute of Mathematical Sciences, ShanghaiTech University, Shanghai 201210, China |
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发表于 2024-1-22 11:40:47
