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

Published online by Cambridge University Press:  17 February 2009

John R. Cannon  and
George H. Knightly
John R. Cannon
Affiliation:
Washington State University, Pullman, Washingtom 99164, U.S.A.
George H. Knightly
Affiliation:
University of Massachusetts, Amherst, Massachusetts 01003, U.S.A.
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Abstract

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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

holds for 0 < t ≤ T and certain real numbres C, β > 0.

Type
Research Article
Information
The ANZIAM Journal , Volume 29 , Issue 4 , April 1988 , pp. 440 - 447
Copyright
Copyright © Australian Mathematical Society 1988

References

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