Abstract

Turbulence, a phenomenon observed by physicists in natural and laboratory flows, is thought to be described by Navier-Stokes equations (NSE). Mathematicians are wondering whether NSE are well posed, namely whether they can develop a singularity in finite time from regular initial conditions. Given that, it is natural to investigate regularity properties of turbulence. In this talk, I will review available tools to investigate statistical and deterministic regularity of turbulent flows, some of which are directly inspired from regularity tools developed by mathematicians for NSE . I will also describe the results of application of such tools to numerical simulations of NSE or to state-of-the art experimental measurements and discuss their link and potential implication regarding regularity properties of NSE .