Navier-Stokes equations in the whole space with an eddy viscosity

被引：1
|
作者：
Lewandowski, Roger [1 ,2 ]
机构：
[1] Univ Rennes 1, IRMAR, UMR 6625, Campus Beaulieu, F-35042 Rennes, France
[2] INRIA, Fluminance Team, Campus Beaulieu, F-35042 Rennes, France
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 478卷 / 02期
关键词：
Navier-Stokes equations; Eddy viscosities; Turbulent solutions; LERAY-ALPHA MODEL; WEAK SOLUTIONS; LANS-ALPHA; OSCILLATIONS; FLUID; TERMS;
D O I：
10.1016/j.jmaa.2019.05.051
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the Navier-Stokes equations with an extra eddy viscosity term in the whole space R-3. We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove that when the regularizing parameter goes to zero, the solution of the regularized system converges to a turbulent solution of the initial system. (C) 2019 Elsevier Inc. All rights reserved.
引用
收藏
页码：698 / 742
页数：45
相关论文
共 50 条
  • [1] Vanishing viscosity limit for Navier-Stokes equations with general viscosity to Euler equations
    Zhang, Tingting
    APPLICABLE ANALYSIS, 2018, 97 (11) : 1967 - 1982
  • [2] NUMERICAL ANALYSIS OF MODULAR VMS METHODS WITH NONLINEAR EDDY VISCOSITY FOR THE NAVIER-STOKES EQUATIONS
    Shan, Li
    Layton, William J.
    Zheng, Haibiao
    INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2013, 10 (04) : 943 - 971
  • [3] Semi-Implicit Schemes for Transient Navier-Stokes Equations and Eddy Viscosity Models
    Davis, Lisa G.
    Pahlevani, Faranak
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2009, 25 (01) : 212 - 231
  • [4] ESTIMATES FOR THE NAVIER-STOKES EQUATIONS IN THE HALF-SPACE FOR NONLOCALIZED DATA
    Maekawa, Yasunori
    Miura, Hideyuki
    Prange, Christophe
    ANALYSIS & PDE, 2020, 13 (04): : 945 - 1010
  • [5] Generalized Navier-Stokes equations with nonlinear anisotropic viscosity
    de Oliveira, H. B.
    ANALYSIS AND APPLICATIONS, 2019, 17 (06) : 977 - 1003
  • [6] On the Navier-Stokes equations with variable viscosity in a noncylindrical domain
    de Araujo, G. M.
    Miranda, M. Milla
    Medeiros, L. A.
    APPLICABLE ANALYSIS, 2007, 86 (03) : 287 - 313
  • [7] PRECONDITIONING THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITH VARIABLE VISCOSITY
    He, Xin
    Neytcheva, Maya
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2012, 30 (05) : 461 - 482
  • [8] Time and Space parallelization of the Navier-Stokes equations
    Albarreal Nunez, Isidoro I.
    Calzada Canalejo, M. Carmen
    Cruz Soto, Jose Luis
    Fernandez Cara, Enrique
    Galo Sanchez, Jose R.
    Marin Beltran, Mercedes
    COMPUTATIONAL & APPLIED MATHEMATICS, 2005, 24 (03): : 417 - 438
  • [9] Partial and full hyper-viscosity for Navier-Stokes and primitive equations
    Hussein, Amru
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (04) : 3003 - 3030
  • [10] FRACTIONAL NAVIER-STOKES EQUATIONS
    Cholewa, Jan W.
    Dlotko, Tomasz
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2018, 23 (08): : 2967 - 2988
12345