Global attractor for the Navier-Stokes equations with fractional deconvolution

被引：4

作者：

Catania, Davide ^{[1
,2
]}

Morando, Alessandro ^{[1
]}

Trebeschi, Paola ^{[1
]}

机构：

[1] Univ Brescia, Sez Matemat, DICATAM, I-25133 Brescia, Italy

[2] Univ eCampus, Fac Ingn, I-22060 Novedrate, CO, Italy

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2015年 / 22卷 / 04期

关键词：

Navier-Stokes equations; Global attractor; Fractal and Hausdorff dimension; Approximate deconvolution models (ADM) and methods; Fractional filter; Large eddy simulation (LES); TURBULENCE; MODELS; EXISTENCE;

D O I：

10.1007/s00030-014-0305-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a large eddy simulation model for the 3D Navier-Stokes equations obtained through fractional deconvolution of generic order. The global well-posedness of such a problem is already known. We prove the existence of the global attractor for the solution operator and find estimates for its Hausdorff and fractal dimensions both in terms of the Grashoff number and in terms of the mean dissipation length, with particular attention to the dependence on the fractional and deconvolution parameters. These results can be interpreted as bounds for the number of degrees of freedom of long-time dynamics, thus providing further information on the validity of the model for the simulation of turbulent 3D flows.

引用

页码：811 / 848

页数：38

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