A quasi-steady-state apprcncimation to the Navier-Stokes equation is the corresponding equation with nonhomogeneous forcing term f(x, t), but with the term Vt deleted. For solutions that are zero on the boundary, the difference z between the solution of the Navier-Stokes equation and the solution of this quasi-steady-state approximation is estimated in the L2 norm ║z║ with respect to the spatial variables. For sufficiently large viscosity or sufficiently small body force f, the inequality
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0334270000005932/resource/name/S0334270000005932_eqnU1.gif?pub-status=live)
holds for 0 < t ≤ T and certain real numbres C, β > 0.