Abstract: In this talk, I will discuss some recent results about the asymptotic stability of Couette flow for 2D and 3D Stokes-transport equations. The Stokes-transport equation serves as a reduced model for oceanography and sedimentation. The density is transported by the velocity field, satisfying the momentum balance between viscosity, pressure, and gravity effects, described by the Stokes equation at any given time. We found the inviscid damping type decay of the velocity for both 2D and 3D models. In the 3D model, we also carefully treat the lift-up effect. The talk is based on joint works with Daniel Sinambela and Ruizhao Zi.
