From AMS Glossary
(Also called steady motion, stationary motion.) A fluid motion in which the velocities at every point of the field are independent of time; streamlines and trajectories are identical.
Sometimes it is further assumed that all other properties of the fluid (pressure, density, etc.) are also independent of time. All local derivatives in the fundamental equations then vanish. A steady-state solution to a theoretical problem suggests two further questions: how the steady state came to exist (the initial-value problem), and whether it will persist (the instability problem).