Remark on the stability of the large stationary solutions to the Navier–Stokes equations under the general flux condition

Consider stationary weak solutions of the Navier–Stokes equations in a bounded domain in R 3 under the nonhomogeneous boundary condition. We give a new approach for the stability of the stationary flow in the L 2 -framework. Furthermore, we give some examples of stable solutions which may be large in L 3 ( Ω ) or W 1 , 3 / 2 ( Ω ) .