Intermittency and Dissipation

Intermittency is a remarkable feature of three-dimensional turbulence for which we still lack explanation from first principles. After a brief review on the main mathematical achievements on turbulence, and after defining what we mean by "intermittency", it will be shown how a dissipation with a non-trivial lower-dimensional part induces a quantitative intermittent regularity of the weak solution. The result is in fact more general than that, providing an optimal space-time regularity of the local dissipation measure in a negative Besov space.