3 papers
math.AP2025
Sharp uniform-in-diffusivity mixing rates for passive scalars in parallel shear flows
Dallas Albritton, Rajendra Beekie
We consider the advection-diffusion equation describing the evolution of a passive scalar in a background shear flow. We prove the optimal uniform-in-diffusivity mixing rate $\| f…
math.AP2024
Transition Threshold for Strictly Monotone Shear Flows in Sobolev Spaces
Rajendra Beekie, Siming He
We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on with small viscosity . We…
math.AP2024
Uniform vorticity depletion and inviscid damping for periodic shear flows in the high Reynolds number regime
Rajendra Beekie, Shan Chen, Hao Jia
We study the dynamics of the two dimensional Navier-Stokes equations linearized around a shear flow on a (non-square) torus which possesses exactly two non-degenerate critical poin…