Statistical solutions and Onsager’s conjecture. (English) Zbl 1398.35153

Summary: 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 the first author et al. [Arch. Ration. Mech. Anal. 226, No. 2, 809–849 (2017; Zbl 1373.35193)]. 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.


35Q31 Euler equations
76M35 Stochastic analysis applied to problems in fluid mechanics
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35D30 Weak solutions to PDEs


Zbl 1373.35193
Full Text: DOI arXiv


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