Statistical solutions and Onsager's conjecture

PHYSICA D-NONLINEAR PHENOMENA

卷:376

Article

Fjordholm, U. S.¹  Wiedemann, E.² 

[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

关键词: Incompressible Euler equations;    Onsager's conjecture;    Statistical solutions;    Energy conservation;   

DOI  :  10.1016/j.physd.2017.10.009

来源: Elsevier

【 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.

【 授权许可】

Free