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."

引用

页码：567 / 600

页数：34

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