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Published online by Cambridge University Press: 15 August 2019
This contribution covers the topic of my talk at the 2016-17 Warwick-EPSRC Symposium: 'PDEs and their applications'. As such it contains some already classical material and some new observations. The main purpose is to compare several avatars of the Kato criterion for the convergence of a Navier-Stokes solution, to a regular solution of the Euler equations, with numerical or physical issues like the presence (or absence) of anomalous energy dissipation, the Kolmogorov 1/3 law or the Onsager C^{0,1/3} conjecture. Comparison with results obtained after September 2016 and an extended list of references have also been added.
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