Phragmen-Lindelöf alternative results for the initial boundary problem of stokes equation
In this paper we prove Phragmén-Lindelöf type alternative for the initial boundary problem of Stokes equation, i. e. we show that the energy expression for the solution of the initial boundary problem must either grow exponentially or decay exponentially with axial distance from the end of a semi-infinite strip. For the case of decay, we also establish the pointwise estimate for the maximum module of the Stokes flow and present a method for obtaining explicit bounds for the total energy.
Key wordsStokes equation initial boundary problem phragmén-Lindelöf alternative theorem estimate of energy dissipation
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