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In this paper,we derive estimates for weighted energy expression for the solution of the Stokes flow equation in a semi-infinite plane channel by means of a second order differential inequality.From the estimates ,we establish Phragmen-Lindelof alternative that the solutions either grow or decay exponentially.In the case of decay,we also show how to bound the total weighted energy. Mathematics subject classification (2000): 35B40, 35K50, 35K45.

Phragmén-Lindelöf type alternative results for the stokes flow equation