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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.

MSC:

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

Citations:

Zbl 1373.35193
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References:

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