Stoxes方程初边值问题的Phragmen－Lindelof二择性原理

Phragmen-Lindelof Alternative Results for the Initial Boundary Problem of Stokes Equation

本文对非定常的Ｓｔｏｋｅｓ方程的初边值问题证明了Ｐｈｒａｇｍｅｎ－Ｌｉｎｄｅｌｏｆ二择性原理，即证明Ｓｔｏｋｅｓ流函数的能量，随着与带状区域有限端距离的增加必定或者按指数率增长或者按指数率衰减．对能量衰减情况建立了Ｓｔｏｋｅｓ流速度的最大模的点点估计．并提出求全能量上界的方法．

In this paper we prove Phragmen-Lindelof 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 ordecay 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 maximummodule of the Stokes flow and present a method for obtaining explicit bounds for the total energy.