Some remarks on a quasi-steady-state approximation of the Navier-Stokes equation

John R. Cannon, George H. Knightly
1988 The Journal of the Australian Mathematical Society Series B Applied Mathematics  
A quasi-steady-state approximation to the Navier-Stokes equation is the corresponding equation with nonhomogeneous forcing term f(z,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-steadystate approximation is estimated in the L% norm ||z|| with respect to the spatial variables. For sufficiently large viscosity or sufficiently small body force f, the inequality
more » ... e inequality ||z(.,t)|| 2 <||z(.,0)|| 2 exp{-/3«} + C sup ||f(|| 0 0.
doi:10.1017/s0334270000005932 fatcat:qjgvd2lp5fbpfglfirlynl7iqi