Statistical solutions and Onsager's conjecture

被引：33

作者：

Fjordholm, U. S. ^{[1
]}

Wiedemann, E. ^{[2
]}

机构：

[1] Univ Oslo, Dept Math, Postboks 1053 Blindern, N-0316 Oslo, Norway

[2] Leibniz Univ Hannover, Inst Angew Math, Welfengarten 1, D-30167 Hannover, Germany

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2018年 / 376卷

关键词：

Incompressible Euler equations; Onsager's conjecture; Statistical solutions; Energy conservation; MEASURE-VALUED SOLUTIONS; NAVIER-STOKES EQUATIONS; ENERGY-CONSERVATION; WEAK SOLUTIONS; EULER EQUATIONS; DISSIPATION; LAWS;

D O I：

10.1016/j.physd.2017.10.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a version of Onsager's conjecture on the conservation of energy for the incompressible Euler equations in the context of statistical solutions, as introduced recently by Fjordholm et al. (2017). As a byproduct, we also obtain an alternative proof for the conservative direction of Onsager's conjecture for weak solutions, under a weaker Besov-type regularity assumption than previously known. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：259 / 265

页数：7

共 50 条

[21] The Onsager conjecture in 2D: a Newton-Nash iteration [J].

Giri, Vikram ;

Radu, Razvan-Octavian .

INVENTIONES MATHEMATICAE, 2024, 238 (02) :691-768

[22] LECTURES ON THE ONSAGER CONJECTURE [J].

Shvydkoy, Roman .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2010, 3 (03) :473-496

[23] On the inviscid limit of the compressible Navier-Stokes equations near Onsager's regularity in bounded domains [J].

Chen, Robin Ming ;

Liang, Zhilei ;

Wang, Dehua ;

Xu, Runzhang .

SCIENCE CHINA-MATHEMATICS, 2024, 67 (01) :1-22

[24] On the Extension of Onsager’s Conjecture for General Conservation Laws [J].

Claude Bardos ;

Piotr Gwiazda ;

Agnieszka Świerczewska-Gwiazda ;

Edriss S. Titi ;

Emil Wiedemann .

Journal of Nonlinear Science, 2019, 29 :501-510

[25] On the Extension of Onsager's Conjecture for General Conservation Laws [J].

Bardos, Claude ;

Gwiazda, Piotr ;

Swierczewska-Gwiazda, Agnieszka ;

Titi, Edriss S. ;

Wiedemann, Emil .

JOURNAL OF NONLINEAR SCIENCE, 2019, 29 (02) :501-510

[26] An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations [J].

Drivas, Theodore D. ;

Eyink, Gregory L. .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2018, 359 (02) :733-763

[27] Remarks on the "Onsager Singularity Theorem" for Leray-Hopf Weak Solutions: The Holder Continuous Case [J].

Berselli, Luigi C. .

MATHEMATICS, 2023, 11 (04)

[28] The Onsager theory of wall-bounded turbulence and Taylor's momentum anomaly [J].

Eyink, Gregory L. ;

Kumar, Samvit ;

Quan, Hao .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2022, 380 (2218)

[29] An Onsager singularity theorem for Leray solutions of incompressible Navier-Stokes [J].

Drivas, Theodore D. ;

Eyink, Gregory L. .

NONLINEARITY, 2019, 32 (11) :4465-4482

[30] On energy conservation for the hydrostatic Euler equations: an Onsager conjecture [J].

Boutros, Daniel W. ;

Markfelder, Simon ;

Titi, Edriss S. .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2023, 62 (08)

← 1 2 3 4 5 →