Strong convergence of a vector-BGK model to the incompressible Navier-Stokes equations via the relative entropy method

被引：7

作者：

Bianchini, Roberta ^{[1
,2
]}

机构：

[1] UMPA, Ecole Normale Super Lyon, UMR CNRS ENSL 5669, 46 Allee Italie, F-69364 Lyon 07, France

[2] CNR, Ist Applicaz Calcolo Mauro Picone, Via Taurini 19, I-000185 Rome, Italy

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 132卷

关键词：

Vector-BGK models; Discrete-velocity BGK models; Incompressible Navier-Stokes equations; Dissipative entropy; Relative entropy; Diffusive relaxation; DISCRETE KINETIC APPROXIMATION; DISSIPATIVE HYPERBOLIC SYSTEMS; FLUID DYNAMIC LIMITS; RELAXATION SCHEMES; CONSERVATION-LAWS; GLOBAL EXISTENCE; SMOOTH SOLUTIONS;

D O I：

10.1016/j.matpur.2019.04.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to prove the strong convergence of the solutions to a vector-BGK model under the diffusive scaling to the incompressible Navier-Stokes equations on the two-dimensional torus. This result holds in any interval of time [0, T], with T > 0. We also provide the global in time uniform boundedness of the solutions to the approximating system. Our argument is based on the use of local in time H-s-estimates for the model, established in a previous work, combined with the L-2-relative entropy estimate and the interpolation properties of the Sobolev spaces. (C) 2019 Elsevier Masson SAS. All rights reserved.

引用

页码：280 / 307

页数：28

共 50 条

[1] CONVERGENCE OF A VECTOR-BGK APPROXIMATION FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
Bianchini, Roberta
Natalini, Roberto
[J]. KINETIC AND RELATED MODELS, 2019, 12 (01) : 133 - 158
[2] Discrete-Velocity Vector-BGK Models Based Numerical Methods for the Incompressible Navier-Stokes Equations
Zhao, Jin
[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2021, 29 (02) : 420 - 444
[3] Approximation of the multi-dimensional incompressible Navier-Stokes equations by discrete-velocity vector-BGK models
Zhao, Jin
Zhang, Zhimin
Yong, Wen-An
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 486 (02)
[4] Convergence of the relaxed compressible Navier-Stokes equations to the incompressible Navier-Stokes equations
Ju, Qiangchang
Wang, Zhao
[J]. APPLIED MATHEMATICS LETTERS, 2023, 141
[5] Lattice BGK model for incompressible Navier-Stokes equation
Guo, ZL
Shi, BC
Wang, NC
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 165 (01) : 288 - 306
[6] LATTICE BGK MODEL FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATION
Zhang Xiao-jun
[J]. Journal of Hydrodynamics, 2003, (03) : 96 - 102
[7] The incompressible lattice BGK model for Navier-Stokes equation
Zhang, XJ
Liu, ZY
[J]. RECENT ADVANCES IN FLUID MECHANICS, 2004, : 753 - 756
[8] Lattice BGK model for time-fractional incompressible Navier-Stokes equations
Du, Rui
Wang, Yibo
[J]. APPLIED MATHEMATICS LETTERS, 2021, 114
[9] From the BGK model to the Navier-Stokes equations
Saint-Raymond, L
[J]. ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2003, 36 (02): : 271 - 317
[10] Convergence of compressible Navier-Stokes-Maxwell equations to incompressible Navier-Stokes equations
Yang JianWei
Wang Shu
[J]. SCIENCE CHINA-MATHEMATICS, 2014, 57 (10) : 2153 - 2162

← 1 2 3 4 5 →