Point vortex approximation for 2D Navier-Stokes equations driven by space-time white noise

被引：5

作者：

Flandoli, Franco ^{[1
]}

Luo, Dejun ^{[2
,3
]}

机构：

[1] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56124 Pisa, Italy

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

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 493卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Point vortices; Navier-Stokes equations; Space-time white noise; Vorticity formulation; Weak convergence; EULER EQUATIONS; CONVERGENCE; UNIQUENESS;

D O I：

10.1016/j.jmaa.2020.124560

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the system of point vortices, perturbed by a certain transport type noise, converges weakly to the vorticity form of 2D Navier-Stokes equations driven by the space-time white noise. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：21

共 21 条

[1] On numerical approximation of stochastic Burgers' equation [J].

Alabert, A ;

Gyöngy, I .

FROM STOCHASTIC CALCULUS TO MATHEMATICAL FINANCE: THE SHIRYAEV FESTSCHRIFT, 2006, :1-+

[2] Uniqueness of solutions of the stochastic Navier-Stokes equation with invariant measure given by the enstrophy [J].

Albeverio, S ;

Ferrario, B .

ANNALS OF PROBABILITY, 2004, 32 (02) :1632-1649

[3] GLOBAL FLOWS WITH INVARIANT (GIBBS) MEASURES FOR EULER AND NAVIER-STOKES 2-DIMENSIONAL FLUIDS [J].

ALBEVERIO, S ;

CRUZEIRO, AB .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 129 (03) :431-444

[4]

Albeverio S., 2008, CIME LECT

[5] Strong L2 convergence of time numerical schemes for the stochastic two-dimensional Navier-Stokes equations [J].

Bessaih, Hakima ;

Millet, Annie .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2019, 39 (04) :2135-2167

[6]

BILLINGSLEY P., 1999, A Wiley-Interscience Publication, Vsecond

[7] Two-dimensional Navier-Stokes equations driven by a space-time white noise [J].

Da Prato, G ;

Debussche, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 196 (01) :180-210

[8] The 2D-Navier-Stokes equations perturbed by a delta correlated noise [J].

Debussche, A .

PROBABILISTIC METHODS IN FLUIDS, PROCEEDINGS, 2003, :115-129

[9] SEMIGROUP SPLITTING AND CUBATURE APPROXIMATIONS FOR THE STOCHASTIC NAVIER-STOKES EQUATIONS [J].

Doersek, Philipp .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2012, 50 (02) :729-746

[10] 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

← 1 2 3 →