Spatial behavior of solution for the Stokes flow equation
Bull. Korean Math. Soc. 2011 Vol. 48, No. 2, 397-412
https://doi.org/10.4134/BKMS.2011.48.2.397
Printed March 1, 2011
Yan Liu, Wenhui Liao, and Changhao Lin
Guangdong University of Finance, Guangdong University of Finance, South China Normal University
Abstract : 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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