Theodore D. Drivas
Mathematics of incompressible turbulence
Abstract: We will discuss some foundational aspects of three-dimensional incompressible fluid turbulence, including guiding experimental observations, Kolmogorov’s 1941 theory on the structure of a turbulent flow, Onsager’s 1949 conjecture on anomalous dissipation and weak Euler solutions, and Landau’s Kazan remark concerning intermittency. Mathematical constraints on, as well as constructions that exhibit features of turbulent behavior will be discussed.
Alexei A. Mailybaev
Spontaneous stochasticity and RG
Lecture 1: We introduce the phenomenon of spontaneous stochasticity and demonstrate it in different fluid models, descending from the fluctuating Navier-Stokes equations to toy models.
Lecture 2: We show how the Feigenbaum-style renormalization-group (RG) is introduced, characterizing the inviscid limit, its stability and bifurcations.
Lecture 3: We extend the RG approach to the stochastic framework, demonstrating how it describes the joint limit of zero viscosity and noise.
