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Bull. Korean Math. Soc. 2011; 48(2): 397-412

Printed March 1, 2011

https://doi.org/10.4134/BKMS.2011.48.2.397

Copyright © The Korean Mathematical Society.

Spatial behavior of solution for the Stokes flow equation

Yan Liu, Wenhui Liao, and Changhao Lin

Guangdong University of Finance, Guangdong University of Finance, South China Normal University

Abstract

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In this paper, the equation of the transient Stokes flow of an incompressible viscous fluid is studied. Growth and decay estimates are established associating some appropriate cross sectional line and area integral measures. The method of the proof is based on a first-order differential inequality leading to an alternative of Phragm\'{e}n-Lindel\"{o}f type in terms of an area measure of the amplitude in question. In the case of decay, we also indicate how to bound the total energy.

Keywords: spatial behavior, transient Stokes flow, Saint-Venant's principle, biharmonic equation, stream function

MSC numbers: 35B40, 35K10, 35K20

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