Asymptotic stability of Landau solutions to Navier-Stokes system
  It is known that the three dimensional Navier-Stokes system for an incompressible fluid in the whole space has a one parameter family of explicit stationary solutions, which are axisymmetric and homogeneous of degree -1. We show that these solutions are asymptotically stable under any $L^2$-perturbation. 
Grzegorz Karch, Dominika Pilarczyk
math.AP