On mixing for circular flows

In recent years, following the seminal works of Villani and Mouhot on Landau damping, phase-mixing as a damping mechanism and inviscid damping in fluid dynamics have attracted much interest. Here, mixing in physical space and weak convergence interact with the Biot-Savart law and results in damping of the velocity field.

In this talk, I will discuss linear stability and damping with optimal decay rates around 2D Taylor-Couette flow between two concentric cylinders and similar circular flows. A particular focus will be on asymptotic singularity formation at the boundary and stability in weighted spaces.