Mean Field Limit of Point Vortices with Environmental Noises to Deterministic 2D Navier-Stokes Equations

被引：2

作者：

Flandoli, Franco ^{[1
]}

Luo, Dejun ^{[2
,3
]}

机构：

[1] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy

[2] Chinese Acad Sci, Acad Math & Syst Sci, Key Lab RCSDS, Beijing 100190, Peoples R China

[3] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2024年

基金：

中国国家自然科学基金; 国家重点研发计划;

关键词：

Mean field limit; Point vortex; Environmental noise; 2D Navier-Stokes equation; Entropy; EULER EQUATIONS; CHAOS; PROPAGATION; SYSTEMS;

D O I：

10.1007/s40304-024-00406-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider point vortex systems on the two-dimensional torus perturbed by environmental noise. It is shown that, under a suitable scaling of the noises, weak limit points of the empirical measures are solutions to the vorticity formulation of deterministic 2D Navier-Stokes equations.

引用

页数：22

共 30 条

[1] Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds [J].

Arnaudon, Marc ;

Thalmaier, Anton ;

Wang, Feng-Yu .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2009, 119 (10) :3653-3670

[2]

Billingsley P., 1968, Convergence of Probability Measures, DOI DOI 10.1002/9780470316962

[3] Sharp nonuniqueness for the Navier-Stokes equations [J].

Cheskidov, Alexey ;

Luo, Xiaoyutao .

INVENTIONES MATHEMATICAE, 2022, 229 (03) :987-1054

[4] Regularized vortex approximation for 2D Euler equations with transport noise [J].

Coghi, Michele ;

Maurelli, Mario .

STOCHASTICS AND DYNAMICS, 2020, 20 (06)

[5] PROPAGATION OF CHAOS FOR INTERACTING PARTICLES SUBJECT TO ENVIRONMENTAL NOISE [J].

Coghi, Michele ;

Flandoli, Franco .

ANNALS OF APPLIED PROBABILITY, 2016, 26 (03) :1407-1442

[6] Full well-posedness of point vortex dynamics corresponding to stochastic 2D Euler equations [J].

Flandoli, F. ;

Gubinelli, M. ;

Priola, E. .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2011, 121 (07) :1445-1463

[7] Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations [J].

Flandoli, Franco ;

Galeati, Lucio ;

Luo, Dejun .

JOURNAL OF EVOLUTION EQUATIONS, 2021, 21 (01) :567-600

[8] CONVERGENCE OF TRANSPORT NOISE TO ORNSTEIN-UHLENBECK FOR 2D EULER EQUATIONS UNDER THE ENSTROPHY MEASURE [J].

Flandoli, Franco ;

Luo, Dejun .

ANNALS OF PROBABILITY, 2020, 48 (01) :264-295

[9]

Flandoli F, 2019, PROBAB THEORY REL, V175, P783, DOI 10.1007/s00440-019-00902-8

[10] Propagation of chaos for the 2D viscous vortex model [J].

Fournier, Nicolas ;

Hauray, Maxime ;

Mischler, Stephane .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2014, 16 (07) :1423-1466

← 1 2 3 →