Inviscid dyadic model of turbulence: The fixed point and Onsager's conjecture

被引：33

作者：

Cheskidov, Alexey ^{[1
]}

Friedlander, Susan

Pavlovic, Natasa

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

[3] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2007年 / 48卷 / 06期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1063/1.2395917

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the three-dimensional scaling of the quadratic nonlinearity. It is proved that the system with forcing has a unique equilibrium and that every solution blows up in finite time in H-5/6 norm. Onsager's [Nuovo Cimento 6, 279-287 (1949)] conjecture is confirmed for the model system. (c) 2007 American Institute of Physics.

引用

页数：16

共 20 条

[11] Finite time blow-up for a Dyadic model of the Euler equations [J].

Katz, NH ;

Pavlovic, N .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (02) :695-708

[12] A cheap Caffarelli-Kohn-Nirenberg inequality for the Navier-Stokes equation with hyper-dissipation [J].

Katz, NH ;

Pavlovic, N .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2002, 12 (02) :355-379

[13]

Kiselev A, 2005, INT MATH RES NOTICES, V2005, P2315

[14] THE LOCAL-STRUCTURE OF TURBULENCE IN INCOMPRESSIBLE VISCOUS-FLUID FOR VERY LARGE REYNOLDS-NUMBERS [J].

KOLMOGOROV, AN .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1991, 434 (1890) :9-13

[15]

MATTINGLY JC, UNPUB SIMPLE SYSTEMS

[16] TEMPORAL INTERMITTENCY IN THE ENERGY CASCADE PROCESS AND LOCAL LYAPUNOV ANALYSIS IN FULLY-DEVELOPED MODEL TURBULENCE [J].

OHKITANI, K ;

YAMADA, M .

PROGRESS OF THEORETICAL PHYSICS, 1989, 81 (02) :329-341

[17]

Onsager L., 1949, NUOVO CIMENTO SUPPL, V6, P279, DOI [10.1007/BF02780991, 10.1007/BF02780988, DOI 10.1007/BF02780988, DOI 10.1007/BF02780991]

[18]

Robert R, 2003, HANDBOOK OF MATHEMATICAL FLUID DYNAMICS, VOL II, P1

[19] On some dyadic models of the Euler equations [J].

Waleffe, F .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 134 (10) :2913-2922

[20] WAVELET-BASED MODEL FOR SMALL-SCALE TURBULENCE [J].

ZIMIN, V ;

HUSSAIN, F .

PHYSICS OF FLUIDS, 1995, 7 (12) :2925-2927

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