Enhanced Dissipation and Transition Threshold for the Poiseuille Flow on $\mathcal{T}\times\mathcal{R}$

Mixing in fluid flows is a complex phenomenon that can be studied from a mathematical point of view. In this talk, we present how mixing can help us understand the dissipation of energy and the stability of solutions. In particular, we study perturbations of the 2D Poiseuille flow and we give some results on enhanced dissipation and on the long time limit. On a more technical level, we prove that the enhanced dissipation rate is proportional to $\nu{1/2}$ and the transition threshold is $\nu{2/3}$.

This talk is part of the Junior Analysis and PDE seminar series.