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 R3R3 under the nonhomogeneous boundary condition. We give a new approach for the stability of the stationary flow in the L2L2-framework. Furthermore, we give some examples of stable solutions which may be large in L3(Ω)L3(Ω) or W1,3/2(Ω)W1,3/2(Ω).