Abstract

In this survey-style talk I discuss the (old) idea of studying turbulence in stochastically-forced fluid equations. I will discuss  definitions of chaos, anomalous dissipation, and various other predictions by physicists that can be phrased as mathematically precise conjectures in this context. Then, I will discuss some recent work by my collaborators and I on various aspects, namely (1) a straightforward characterization of anomalous dissipation that implies the classical Kolmogorov 4/5 law for 3d NSE (joint with Michele Coti Zelati, Sam Punshon-Smith, and Franziska Weber); (2) the study of “Lagrangian chaos” and exponential mixing of scalars and how it leads to a proof of anomalous dissipation and of the power spectrum predicted by Batchelor in 1959 for the simpler problem of Batchelor-regime passive scalar turbulence (joint with Alex Blumenthal and Sam Punshon-Smith); (3) the more recent proof of “Eulerian chaos” for Galerkin truncations of the Navier-Stokes equations (joint with Alex Blumenthal and Sam Punshon-Smith).