Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations

被引：27
|
作者：
Flandoli, Franco [1 ]
Galeati, Lucio [2 ]
Luo, Dejun [3 ,4 ]
机构：
[1] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56124 Pisa, Italy
[2] Univ Bonn, Inst Appl Math, Endenicher Allee 60, D-53115 Bonn, Germany
[3] Chinese Acad Sci, Key Lab RCSDS, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2021年 / 21卷 / 01期
基金：
中国国家自然科学基金;
关键词：
2D Euler equations; Vorticity; Transport noise; Scaling limit; 2D Navier-Stokes equations; DIFFERENTIAL-EQUATIONS; INVARIANT MEASURE; FLOWS; CONTINUITY; UNIQUENESS;
D O I：
10.1007/s00028-020-00592-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with transport-type noises and L-2-initial data. Under a suitable scaling of the noises, we show that the solutions converge weakly to that of the deterministic 2D Navier-Stokes equations. Consequently, we deduce that the weak solutions of the stochastic 2D Euler equations are approximately unique and "weakly quenched exponential mixing."
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页码：567 / 600
页数：34
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