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

1988
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The Journal of the Australian Mathematical Society Series B Applied Mathematics
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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 ||z(.,t)|| 2 <||z(.,0)|| 2 exp{-/3«} + C sup ||f(|| 0 0.

doi:10.1017/s0334270000005932
fatcat:qjgvd2lp5fbpfglfirlynl7iqi