##### Department of Mathematics,

University of California San Diego

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### MATH 248 Seminar In Real Analysis

## Prof. Jacob Bedrossian

#### UCLA

## Chaos and turbulence in stochastic fluid mechanics: What is it and how could we study it?

##### 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).

Host: Prof. Andrej Zlatos

### June 6, 2023

### 11:00 AM

APM 7321

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